# Mathematical Physics group

York has a large and friendly mathematical physics group with a wide range of research interests and an international outlook, with graduate students and researchers from many countries choosing to work here. If you are interested in graduate study or post-doctoral research, please contact the relevant member of staff.

• ## Research in Mathematical Physics

The main areas of research are Quantum Gravity, Quantum Field Theory and Integrable Models, Quantum Information and Foundations of Quantum Mechanics, and Quantum Groups.

• ## Group Members

Information about the staff members and research fellows, graduate students and visitors in our group.

• ## Seminars

The group has two seminars every week. These are very lively with many questions and active participation by the graduate students.

• ## Publications

You will find links to recent publications of the group from these pages.

• ## Visitors

Scientists that have visited our group at York.

• ## Research meetings

We participate in, and help organize, various series of research meetings, including NBMPS, BritGrav and ICFT.

# Group Members

## Staff in Mathematical Physics

Dr Henning Bostelmann
Dipl. Phys., Dr. rer. nat. (Göttingen); Master of Computer Science (Hagen)
Algebraic quantum field theory, operator algebras
+44 1904 32 3088
henning.bostelmann@york.ac.uk
Professor Paul Busch
Dipl.-Phys.(MSc, Cologne), Dr.rer.nat.(Cologne)
Quantum mechanics, foundations, quantum measurement and information, quantum theory and relativity.
+44 1904 32 3082
paul.busch@york.ac.uk
Dr Roger Colbeck
PhD (Cambridge)
quantum information theory, foundations of quantum mechanics
+44 1904 32 3093
roger.colbeck@york.ac.uk
Professor Ed Corrigan
MA, PhD (Cantab), FRS
Quantum field theory, integrable systems, solitons, defects
+44 1904 43 3074
ec9@york.ac.uk
Dr Pierre-Philippe Dechant
BA/MA (Cantab), CASM/MMath (Cantab), PhD (Cantab)
Symmetries, Viruses; Group theory, Coxeter groups, Lie algebras, Clifford algebras, gravitational and particle physics, Moonshine
+44 1904 32 5370
pd583@york.ac.uk
Dr Gustav W Delius
PhD (Stony Brook)
Stochastic Modelling in Mathematical Biology and Theoretical Ecology, Spatial Stochastic Processes, Quantum Field Theory, Integrable Systems, Quantum Groups
+44 1904 32 3077
gustav.delius@york.ac.uk
Professor Chris Fewster
MA, PhD (Cantab)
Mathematical issues in quantum and gravitational physics. Quantum field theory in curved spacetime. Algebraic quantum field theory.
+44 1904 32 3091
chris.fewster@york.ac.uk
Dr Eli Hawkins
PhD (Penn State, Physics), PhD (Penn State, Mathematics)
+44 1904 32 3069
eh555@york.ac.uk
Dr Atsushi Higuchi
BSc (Tokyo), MSc (Kyoto), PhD (Yale)
Quantum field theory, general relativity.
+44 1904 32 3089
atsushi.higuchi@york.ac.uk
Professor Bernard S. Kay
MA (Cantab), PhD (London)
quantum fields, quantum gravity, fundamental problems in quantum theory
+44 1904 32 3092
bernard.kay@york.ac.uk
Prof. Niall MacKay
BA (Cambridge), PhD (Durham)
Integrable quantum field theory, quantum groups
+44 1904 32 3493
niall.mackay@york.ac.uk
Dr Kasia Rejzner
mathematical structures relevant for quantum field theory
+44 1904 32 4153
kasia.rejzner@york.ac.uk
Professor Evgeny Sklyanin
MSc, PhD (Steklov Institute, St Petersburg), FRS
Quantum and classical integrable systems, quantum groups
+44 1904 32 4162
eks2@york.ac.uk
Professor Reidun Twarock
MSc (Bath), PhD (Clausthal, Germany)
Mathematical Biology, Mathematical Physics
+44 1904 32 5368
rt507@york.ac.uk
Dr Stefan Weigert
PD Dr (Basel/CH)
quantum foundations and quantum information: mutually unbiased bases, quantum state reconstruction; PT-symmetry
+44 1904 32 4152
slow500@york.ac.uk

## Ph.D. students in Mathematical Physics

Name Degree information Phone E-mail
Johannes Biniok MPhys (St Andrews) +44 1904 32 3075 jcgb500@york.ac.uk
Thomas Bullock MPhys (Sheffield) +44 1904 32 3075 tjb525@york.ac.uk
Alejandro De La Rosa Gomez BSc (Wisconsin), MSc (Imperial) +44 1904 32 3845 alrg500@york.ac.uk
Jacob Dyer BA (Cantab), MSci (Cantab) +44 1904 32 3085 jpd514@york.ac.uk
Jos Gibbons +44 1904 32 3845 jg1047@york.ac.uk
Daniel Hills MMath (York) +44 1904 32 3075 dh579@york.ac.uk
Spiros Kechrimparis BSc, MSc (Patras) +44 1904 32 3844 sk864@york.ac.uk
Umberto Lupo BSc (Warwick), MASt (Cantab) +44 1904 32 3075 ul504@york.ac.uk
Robert Parini MSci (Dunelm) +44 1904 32 XXXX rp910@york.ac.uk
Mirjam Weilenmann BSc & MSc (ETH, Zurich) +44 1904 32 XXXX msw518@york.ac.uk
Francis Wingham MSci (Nottingham) +44 1904 32 XXXX flw508@york.ac.uk

# Former Research Students in Mathematical Physics

## Research students since 2000

 Dan McNulty, PhD 2013Mutually unbiased product basesSupervisor: Stefan Weigert Matthew Ferguson, PhD 2013Aspects of dynamical locality and locally covariant canonical quantizationSupervisor: Chris Fewster David Hunt, PhD 2013The quantization of linear gravitational perturbations and the hadamard conditionSupervisor: Chris Fewster Leon Loveridge, PhD 2013Quantum measurements in the presence of symmetrySupervisor: Paul Busch Vidas Regelskis, PhD 2013Quantum algebras and integrable boundaries in AdS/CFTSupervisor: Niall MacKay David Bullock, PhD 2012Klein-Gordon solutions on non-globally hyperbolic standard static spacetimesSupervisor: Bernard Kay Leonardo Ortiz, PhD 2012Quantum fields on BTZ black holesSupervisor: Bernard Kay Faisal Mir, PhD 2011Perturbative quantum gravity and Yang-Mills theories in de Sitter spacetimeSupervisor: Atsushi Higuchi Charlie Dyson, MSc 2011Implementing quantum algorithms using classical electrical circuits : Deutsch, Deutsch-Jozsa and GroverSupervisor: Stefan Weigert Paul Melvin, PhD 2010Twist deformed manifolds and cosmologySupervisor: Ed Corrigan Stephen Brierley, PhD 2010Mutually unbiased bases in low dimensionsSupervisor: Stefan Weigert Yen-Cheong Lee, PhD 2010Classical and quantum field theory in de Sitter expanding universeSupervisor: Atsushi Higuchi Jacobus Sanders, PhD 2009Aspects of locally covariant quantum field theorySupervisor: Chris Fewster Joseph Hilling, M.Phil. 2009Pure, finite entanglement and properties of hypermatricesSupervisor: Tony Sudbery Paul Butterley, PhD 2008Topics in quantum information theorySupervisor: Tony Sudbery William Hall, PhD 2008A study of entanglement and its role in quantum information theorySupervisor: Tony Sudbery Peter Larkin, PhD 2008Pre-holographySupervisor: Bernard Kay Lutz Osterbrink, PhD 2008 Averaged Energy Inequalities for the Non-minimally coupled scalar field Supervisor: Chris Fewster Sikarin Yoo-Kong, MSc 2008 Towards an Entanglement Measure based on the Partial TransposeSupervisor: Stefan Weigert Ko Sanders, PhD 2008 Aspects of Locally Covariant Quantum Field Theory Supervisor: Chris Fewster Giles Martin, PhD 2007Classical and quantum radiation reactionSupervisor: Atsushi Higuchi Lieven Clarisse, PhD 2006Entanglement distillation : a discourse on bound entanglement in quantum information theorySupervisor: Tony Sudbery David Emms, PhD 2006Analysis of graph structure using quantum walksSupervisor: Edwin Hancock Barry Miller, PhD 2006 Supergroup sigma modelsSupervisor: Niall MacKay Calvin Smith, PhD 2006 Energy Conditions in Quantum Field TheorySupervisor: Chris Fewster Varqa Abyaneh, PhD 2005Gravitationally induced decoherenceSupervisor: Bernard Kay Joseph Hilling, PhD 2005 Quantum Information and Quantum ComputingSupervisor: Tony Sudbery Emily King, M.Phil. 2005Quantization of a dynamical system with constraints forming an sl(2,R) AlgebraSupervisor: Atsushi Higuchi Simon Dawson, PhD 2004 Bounds on Negative Energy Densities in Quantum Field Theories on Flat and Curved SpacetimesSupervisor: Chris Fewster Alan George, PhD 2004Exactly solvable field theories with boundariesSupervisor: Gustav W Delius Cristina Zambon, PhD 2004Defects and other boundaries in integrable field theoriesSupervisor: Ed Corrigan Richard Weeks, PhD 2004The physical graviton two-point function in de Sitter spacetime withS3 spatial sectionsSupervisor: Atsushi Higuchi Ukyo Kono, MSc 2004Supervisor: Niall MacKay Jason Szulc, PhD 2003Topics in quantum informationSupervisor: Tony Sudbery Ben Short, PhD 2003Particle scattering in the principal chiral model on a half-lineSupervisor: Niall MacKay Brett Gibson, PhD 2001Boundary states in low rank ATFTs on the half-lineSupervisor: Gustav W Delius Spyros Kouris, PhD 2001On linearised quantum gravity in de Sitter spacetimeSupervisor: Atsushi Higuchi Chris Barton, PhD 2000Magic squares of lie algebras.Supervisor: Tony Sudbery Hilary Carteret, PhD 2000Symmetry and multiparticle entanglement.Supervisor: Tony Sudbery Stefan Hollands, PhD 2000Aspects of quantum field theory in curved spacetime.Supervisor: Bernard Kay Alfredo Calvo-Pereira, MSc 2000Quantum Inequalities in Flat and Curved SpacetimesSupervisor: Chris Fewster

# Former Staff and Postdocs

This page lists past members of the Mathematical Physics group who have left since summer 2000.

• Dr Anastasia Doikou, Dr Anastasia Doikou, EPSRC Fellow working on integrable spin chains and other solvable statistical systems, moved to Annecy on a postdoc within the EC FP5 Network 'EUCLID', then back to Greece and is now Reader at Heriot-Watt.
• Dr Pascal Baseilhac, Marie-Curie Fellow, who worked on integrable quantum field theories, left to start a postdoctoral fellowship with Ryu Sasaki at the Yukawa Institute in Kyoto in November 2001; he now holds a permanent CNRS position in Tours.
• Dr Nicolai Kitanine, EPSRC PDRA, who worked on integrable lattice models, left to start a postdoctoral fellowship with Michio Jimbo at the University of Tokyo in November 2001; he now holds a permanent position at Cergy-Pontoise.
• Professor Reidun Twarock, Marie-Curie Fellow, moved to a lectureship at the Department of Mathematics at the City University London in March 2001; she was a member of the Statistical Mechanics and Algebra group led by Paul Martin. Her interests have moved towards Mathematical Biology and she is now back at York, first as a Reader jointly in the departments of Mathematics and Biology, and an EPSRC Advanced Fellow, now Professor and member of YCCSA.
• Dr Liu Zhao Visitor from Bo-Yu Hou's group at the Institute of Modern Physics, Northwest University, Xian, China, was here from January to September 2000 on a Royal Society visiting fellowship with additional PPARC support. After leaving York he spent 3 months at the ICTP, Trieste, before returning to Xian.
• Dr Tomasz Brzezinski moved to the Department of Mathematics at Swansea in 2000 with his EPSRC Advanced Research Fellowship and is now a Professor.
• Dr Clare Dunning, EPSRC Fellow, moved to a postdoctoral position at the University of Queensland, Brisbane and is now Senior Lecturer at Kent.
• Dr Mitch Pfenning, EPSRC PDRA, is now an Associate Professor at the United States Military Academy, West Point.
• Dr Davide Fioravanti, Leverhulme Trust, moved to the University of Trento and is now at the University of Bologna.
• Dr Nicolas Crampe, EUCLID RTN Young Researcher, moved to SISSA, Trieste and is now at University of Montpellier 2
• Dr Vincent Caudrelier, EPSRC Research Fellow, now Lecturer at City University.
• Dr Charles Young, PPARC PDRA, moved to the University of Durham and is now Lecturer at the University of Hertfordshire.
• Dr Simone Severini, EPSRC PDRA 2003-6, has moved to the University of Waterloo, Canada.
• Professor Shasanka Roy, EPSRC Visiting Professor 2005-6, has returned to the Tata Institute of Fundamental Research, Mumbai.
• Dr Benoit Vicedo, EPSRC PDRA, is now a Lecturer at the University of Hertfordshire.
• Dr Boris Noyvert, Marie-Curie Fellow, moved to Warwick Systems Biology Centre as a Research Fellow.

# Research in Mathematical Physics

Our research subdivides into four main areas, with many overlaps.

# Quantum Gravity

Staff: H Bostelmann, C Fewster, A Higuchi, B Kay, E Hawkins, K Rejzner;
Research students: J Dyer, J Gibbons, B Lang, U Lupo, J Waldron

# Quantum Integrability

Staff: E Corrigan FRS; G Delius; N MacKay; E Sklyanin FRS;

# Quantum Information & Foundations

Staff: P Busch, R Colbeck, C Fewster, A Higuchi, B Kay, A Sudbery, S Weigert;
Research students: J Biniok, T Bullock, S Kechrimparis, D McNulty, N Stevens

# Quantum Groups

Staff: GW Delius, N MacKay, M Nazarov, E Sklyanin FRS, S Donkin, A Sudbery

Research in Dynamical Systems is done in the Networks and Nonlinear Dynamics Group.

For other research areas in physics please visit the research pages of the Department of Physics.

# Quantum Gravity

The quantum gravity group carries out research on various aspects of quantum gravity as well as on some allied areas of mathematical physics, including certain topics in quantum mechanics and also in classical general relativity. A particular interest of the research group is the subject of quantum field theory in curved spacetime. Our work often makes use of rigorous techniques drawn from functional analysis (e.g. the theory of operators on Hilbert spaces and operator algebras) and other areas of pure mathematics including differential geometry, microlocal analysis and category theory.

While a satisfactory theory of full quantum gravity continues to elude us, the attempt to anticipate some of the properties of such a theory has led to many interesting developments. Especially, Hawking's 1974 prediction of black hole evaporation, which was based on consideration of quantum field theory in curved spacetime, suggests that there must be yet-to-be-discovered deep interconnections between quantum theory, gravity and thermodynamics. More generally, the very existence of the problem of quantum gravity has changed our perspective on each of the separate theories of classical general relativity and quantum field theory and focussed attention on issues (e.g. the problem of singularities in classical general relativity or the problem of locality in quantum field theory) which might be expected to be of relevance for the unification problem. Further, both at the theoretical and experimental/observational level, the two subject areas have now essentially merged, with very-high-energy phenomena believed to have dominated the era just after the big bang and hence to have determined the present structure of the universe.

Recent research by the York group concerns the following issues:

## 1. Quantum field theory in curved spacetime.

Quantum energy inequalities on the renormalised stress-energy tensor.

Most forms of classical matter have a positive energy density, a fact closely related to our experience of gravity as an attractive force. However, the situation is very different in quantum field theory, where the energy density can typically be made as negative as we like. Recent work by Fewster has been directed towards developing "quantum energy inequalities" for quantum fields which show (roughly speaking) that the magnitude and duration of negative energy densities are constrained: the energy density cannot be too negative for too long. An introduction to QEIs and some of the related techniques can be found in Fewster's lecture notes.

Infrared properties of the gravitational field in the Early Universe.

Higuchi, with students Kouris and Weeks, has shown that the growth at long distance of the graviton two-point function in an inflationary spacetime is not reflected in physical two-point functions. He is currently examining claims in the literature that the cosmological constant would be suppressed in such spacetimes due to the above-mentioned growth of the graviton two-point function. See gr-qc/0212031 and references therein. In related work, Fewster and his student Hunt have studied the quantisation of linearised gravity in general cosmological vacuum spacetimes - see

In Minkowski space there is an obvious natural vacuum state for quantum field theory picked out by Poincare invariance. General spacetimes do not have any symmetries and therefore no single natural vacuum state. Instead, a class of physical states is indentified (the Hadamard class). The first fully precise definition of the Hadamard condition was given by Kay and Wald in 1991; not long after that, Radzikowski showed that this condition could be reformulated in terms of microlocal analysis. Work by the York group has extended and refined this formulation; in particular, it plays an important role in Fewster's work on quantum inequalities and was used by Kay in work (with Radzikowski and Wald) on time machine spacetimes (see below). Recently, Fewster and Verch have given a new motivation for the Hadamard class: at least in ultrastatic spacetimes, they showed that any state in which the associated Wick polynomials have finite fluctuations is necessarily Hadamard -see arXiv:1307.5242.

Locally covariant QFT.

Quantum field theory in Minkowski space depends in many ways on the high degree of spacetime symmetry. General curved spacetimes lack any symmetry at all, which makes it hard to prove general statements about general quantum field theories (as opposed to specific models). A major development was the introduction by Brunetti, Fredenhagen and Verch of a locally covariant formulation of QFT in CST based on techniques of category theory. The basic idea is that a theory can be described by a functor from a category of spacetimes to a category of physical systems. Fewster, and his students Lang, Ferguson and Sanders, have worked on various aspects of this formalism, including the formulation of the Dirac theory and a proof of a Reeh-Schlieder theorem (Sanders) and the analysis of when a theory can be thought to describe the same physics in all spacetimes (Fewster [with Verch], Ferguson) as well as studying the effect of spacetime topology on locally covariant theories (Fewster and Lang). Fewster has also shown how the global gauge group of a locally covariant theory can be identified with the automorphism group of the corresponding functor (arXiv:1201.3295). Moreover, a nice consequence of Fewster and Verch's work is a general proof that quantum field theories in curved spacetime do not have natural states, something which had been a "folk theorem" for many years (arXiv:1106.4785).

## 2. Dirac quantisation of general relativity.

General relativity may be regarded as a constrained dynamical system. Although there is a standard method for quantizing constrained systems, due to Dirac, there are obstacles to applying this method to general relativity. There has been a claim that these obstacles can be overcome, and Higuchi is currently trying to determine whether or not this claim is justified.

## 3. Classical limit of radiation reaction in quantum field theory

Higuchi has studied a model in quantum field theory in which one can consider the radiation reaction to a charged particle and then take the classical limit. He found that the result agrees with the standard Lorentz-Dirac theory (quant-ph/0208017). He is currently attempting to compare the radiation reaction in the Lorentz-Dirac theory and that in the quantum theory of a more realistic model.

## 4. Gravitationally induced decoherence.

Kay is presently continuing to work, partly together with Varqa Abyaneh, on a theory (see hep-th/9810077) according to which it is the entanglement between the quantum gravitational field and the quantum state of macroscopic quantum systems which is ultimately responsible for those systems being (with some probability distribution) in one or other of a number of definite spatial configurations. In particular, in the case of Schrodinger's cat this theory offers an explanation as to why the cat has to be either dead or alive.

In the past, other issues investigated by the York group have included:

The theory of the Hawking effect.

In the early 1990s, Kay was involved in proving mathematical theorems which improved our understanding of why it is that - as discovered by Stephen Hawking in 1974 - black holes have to be hot.

The question of whether it is possible in principle to manufacture a "time machine".

Work by the York group has contributed to the present understanding that time machines cannot be manufactured. In particular, Kay has been involved in proving rigorous mathematical theorems (see, e.g., gr-qc/9603012 and gr-qc/9708028) which may be interpreted as telling us that it is impossible to manufacture a time machine which would allow travel to the past by warping spacetime in a way which is describable in terms of the traditional notions of spacetime geometry familiar from Einstein's classical theory of general relativity. These theorems thus tend to lend support to Stephen Hawking's Chronology Protection Conjecture although they don't exclude the possibility of time machines which are so exotic that they warp spacetime in ways which are not describable in classical terms. For a recent overview of the work by Kay mentioned above see gr-qc/0103056.

Other work by the York group has studied the properties of quantum systems on spacetimes containing time machines (setting aside the question of whether such a thing could be manufactured). Kay proposed a weakening of the usual formulation of quantum field theory for such situations; this was further investigated by Fewster and Higuchi (gr-qc/9508051) and then Fewster (gr-qc/9804012). This led to the conclusion that - at least in two dimensions - the proposed framework could not be implemented on generic time machine spacetimes. Other work conducted by Fewster, Higuchi and Wells (gr-qc/9603045) also supports the view that quantum theory (at least as presently understood) cannot generally be formulated in the presence of time machines.

The interaction of black holes with classical & quantum fields.

Higuchi showed that the absorption cross section by a black hole (of arbitrary spacetime dimension) of any kind of massless scalar particle is exactly equal to the horizon area (hep-th/0108144). He also investigated how a charge just outside a black hole responds to Hawking radiation (see gr-qc/0011070 and references therein).

# Quantum Integrability

Ed Corrigan, Gustav Delius, Niall MacKay, Evgeny Sklyanin, Vidas Regelskis

Integrable models are systems in quantum physics which can be solved exactly, because they have a large number of conserved quantities and thus a high degree of symmetry. They appear in many guises - field theories, spin chains, models of statistical mechanics, models of a fixed number of interacting particles - and can also be subsumed into models with even more symmetry, such as conformal field theories and 'superintegrable' models (such as Newtonian gravity and the hydrogen atom!).

The last few decades have seen a resurgence of exactly-solvable physical systems, which appear ubiquitously in modern fundamental physics. For example, they have been at the heart of recent advances in our understanding of the relationship between gauge field theory and string theory, and one of us (Niall MacKay) was an organizer of the research programme on 'Strong Fields, Integrability and Strings' at the Newton Institute, Cambridge in 2007. The mathematical beauty of such models is often seen in new algebraic structures (usually 'quantum groups'), and we have been involved in the discovery and development of many of these.

In our research we typically use classical and first-order quantum ('semiclassical') methods, and try to mesh these together with algebraic techniques which can give exact (to all orders in Planck's constant) results. This gives us a window into many non-perturbative phenomena, such as

• Solitons and Breathers
• Monopoles and Instantons
• Dualities (strong-weak coupling)
• Boundary excitations

To study these we use extended symmetries and principles like

• Non-local and Higher Spin Symmetries
• Quantum Groups and Yangians
• Supersymmetry
• Kac-Moody Algebras and W-Algebras
• S-matrix Factorisation and Bootstrap Principles

Besides their utility in unravelling the non-perturbative structure of two-dimensional quantum field theories these symmetry principles fascinate us because of their intrinsic mathematical beauty. Particular examples of fruitful models are

• Affine Toda Theories (the simplest is the sine-Gordon model)
• The nonlinear Schroedinger and other PDEs
• Principal Chiral Models and Coset Sigma Models
• Perturbed Conformal Field Theories
• Calogero-Sutherland-Moser Models
• Quantum Spin Chains
• Reaction-Diffusion Processes
contributed by Niall Mackay and Gustav Delius

# Quantum Information and Foundations

Quantum Foundations research aims at understanding the puzzling features of quantum theory such as: indeterminacy; the incompatibility of pairs of physical quantities (aka complementarity); the fact that measurements necessarily affect the observed system (aka Heisenberg effect); the strange way in which quantum systems are correlated (aka entanglement); and quantum nonlocality. As well as marking the contrast between quantum and classical physical theories, these features have been found to constitute potentially powerful resources for information processing, thus giving rise to the novel and rapidly developing field of Quantum Information Science, where new paradigms of computation, communication and cryptography are being explored.

Research in the quantum information and foundations group focuses on structural aspects of quantum theory that are relevant to quantum information. Current research themes include:

• Operational quantum physics: structures of the quantum state space and the space of effects and observables, quantum operations
• Quantum State Reconstruction
• Theory of approximate joint measurements of noncommuting observables
• Mutually Unbiased Bases
• Relativistic quantum measurement
• Quantum-classical contrast
• Quantum cryptography

Our group maintains interactions with researchers in the Physics and Computer Science Departments through the Quantum Information Seminar held weekly in term time. Within York, this involves the following researchers as part of the York Centre for Quantum Technologies:

Regional cooperations are facilitated through the White Rose Universities Consortium which sponsors regular quantum information meetings in Leeds, Sheffield and York. International collaborations include the Operational Quantum Physics group at the University of Turku.

News: For current job opportunities see here.

For information about possible PhD projects, see here.

# Quantum Technology Fellowships

## Quantum Technology Fellowships

The Mathematics department at the University of York would like to encourage and support applicants who wish to apply for an EPSRC-funded 5 year quantum technologies fellowship based in York.  These are available at both the 'early career' and 'established career' stages.  Within the department Paul Busch, Roger Colbeck and Stefan Weigert are pursuing research in quantum information and there is further expertise in York in the Physics and Computer Science departments, which are all part of a newly established Centre for Quantum Technologies.  More information about our staff and research can be found at
http://maths.york.ac.uk/www/PhysicsComputing

While we are open to applications for any area relevant to the call, we would particularly welcome those whose research interests include quantum key distribution, quantum randomness generation, quantum metrology or related topics.

There are two deadlines for submission of fellowship proposals and fixed start dates:
* 16:00 on 30 October 2014 [Fixed start date of 01 April 2015]
* 16:00 on 29 January 2015 [Fixed start date of 01 July 2015]

Note that certain eligibility criteria apply, further details of which can be found at
http://www.epsrc.ac.uk/skills/fellows/quantumtechnology/

If you are interested in this opportunity, please make contact with one of us as soon as possible, and at least 1 month before either deadline.

# Quantum Groups

Continuous ('Lie') groups, such as the unitary and orthogonal groups, have been at the heart of the development and classification of new models of particle physics. But at the end of the 1970s hints appeared that, at least in some simple models, there were more subtle algebraic structures, based on Lie groups but deformed in some way dependent on Planck's constant: hence 'quantum' groups. These were set on firm mathematical foundations in the 1980s by Jimbo and by Drinfeld, who later won the Fields medal for this and other work.

Quantum groups appear in many ways in mathematical physics, and especially in integrable models, both of field theory and of statistical mechanics, where they describe various sets of conserved quantities (in an extension of the ideas of spin and isospin), and also appear as purely ('auxiliary') algebraic structures.

Research at York covers this full spectrum, from the construction of quantum groups in terms of fields and physical observables through to a mathematical examination of their structure and representations.

• Yangians
• Quantum Affine Algebras and Superalgebras
• Solutions of the Yang-Baxter equation
• Reflection Equation and associated algebras
• Quantum Lie Algebras
• Non-Commutative Geometry
• Representation Theory, invariants and centralizer algebras

contributed by Niall Mackay

# Mathematical Physics Seminar

The seminars take place on Tuesday lunchtimes at 2:00 pm (mostly internal speakers) and Thursday afternoons from 4:15 pm (mostly external speakers, and preceded by coffee/tea from 4pm), in the relaxed atmosphere of Room G/109 in James College Nucleus. The typical length of the talks is about 1 hour.

## Constructing interacting QFTs via OPEs

Series:
Mathematical Physics Seminar
Date and time:
May 7, 2015, 16:15 - 17:30
Speaker:
Markus Fröb (Leipzig)
Room:
G/109

I will review a new approach to constructing interacting (Euclidean) QFTs in 4 dimensions via the operator product expansion (OPE), and a number of important results that have been proven in the last years using the Polchinski-Kopper flow equation framework, such as existence, convergence and factorisation properties of the OPE in a perturbative sense for non-gauge theories.

Information on How to Reach the University is available. You can locate James College on the campus map. Please contact Eli Hawkins by e-mail if you need further information.

Please also check the Upcoming Events page for other seminars which might be of interest. For example the Departmental Colloquium talks on Wednesdays sometimes are on mathematical physics.

## Programme for this term

Date and time Title Speaker Room
April 16, 2015, 16:00 - 17:15 Gauge theories in locally covariant quantum field theory Alex Schenkel (Heriot Watt) G/109
April 21, 2015, 14:00 - 15:00 Negative energy densities in integrable quantum field theories at one-particle level Henning Bostelmann G/109
May 7, 2015, 16:15 - 17:30 Constructing interacting QFTs via OPEs Markus Fröb (Leipzig) G/109

Please note that this is an evolving programme. It is advisable to (re-load and) re-check the page shortly before each talk. There is a mailing list for the seminar announcements. For further details please contact Eli Hawkins.

Archive of past Mathematical Physics Seminars: 1999-2007, 2007-today.

# Summer 2007

The seminar takes place on Mondays and Thursdays: from 4:20 pm onwards in the very relaxed atmosphere of Room G/109 in Goodricke College. The seminars are preceded by tea from 4 pm. The typical length of the talks is about 1 hour.

• Monday, 30 April 2007, 04:20 PM » 05:20 PM
Title: Gribov copies and confinement
Speaker: Antony Ilderton (University of Plymouth)
Room: G/109
Abstract: I will present an elegant and explicit construction of a wide class of Gribov copies. Although they may be generated infinitesimally, the copies are manifestly non-perturbative. As a consequence it will be demonstrated that the existence of copies provides a non-perturbative justification for the absence of physical coloured charges.
• Monday, 14 May 2007, 04:20 PM » 05:20 PM
Title: Almost quantum theory: classical theories with a constraint on knowledge
Speaker: Robert W. Spekkens (DAMTP, Cambridge)
Room: G/109
Abstract: What kind of theory would be appropriate for an agent living in a world that is essentially classical but where there is a fundamental restriction on how much knowledge can be acquired about the physical state of any system? Formalizing such a restriction, one can define several toy theories that are found to have a rich structure similar to that of quantum theory, including a notion of coherent superposition and entanglement. These theories are also found to have analogues of a wide variety of quantum phenomena, such as complementarity, interference, teleportation, no-cloning, and many quantum cryptographic and communication protocols. The diversity and quality of these analogies provides compelling evidence for the view that quantum states are not states of reality -- as most interpretations suggest -- but rather states of knowledge that are incomplete (and cannot be completed). The question "what is the nature of the reality to which this knowledge refers?" remains open in this research program but the phenomenon of contextuality (a consequence of the Bell-Kochen-Specker theorem) provides, I argue, our best clue for how to answer it.
• Thursday, 24 May 2007, 04:20 PM » 05:20 PM
Title: A New Approach to the Quantum Measurement Problem
Speaker: Geoffrey Sewell (Queen Mary)
Room: G/109
Abstract: The question I shall address is the highly contentious one of whether the traditional form of quantum mechanics, as represented by Schroedinger dynamics and the probabilistic interpretation thereof, covers the measurement process. The problem that arises here is that, whereas the Schroedinger evolution of a system is unitary, its change of state in the measurement process is highly non-unitary (cf. Von Neumann). My treatment of this problem is based on an analysis of the Schroedinger dynamics of the generic conservative model comprising an observed microsystem S and a macroscopic measuring instrument M, whose pointer positions correspond to values of a set of intercommuting macroscopic observables. My main result is that, for a suitable choice of these latter obsrvables and a suitable S-M coupling, the dynamics of the composite (S+M) induces both the change of state of S and the registartion of that change by M demanded by Von Neumann's phenomenological theory of the measurement process. Thus I conclude that the traditional picture of quantum mechanics is complete, in that that the measurement theory does indeed ensue from Schroedinger dynamics together with Born's probabilistic interpretation thereof.
• Thursday, 31 May 2007, 04:20 PM » 05:20 PM
Title: On defects in classical integrable systems
Speaker: Vincent Caudrelier (York)
Room: G/109
Abstract: This talk will be largely introductory. The basic idea is to propose a reformulation of the lagrangian formalism, already presented by Ed Corrigan and Peter Bowcock in previous seminars, to the question of integrable defects in field theories in 1+1 dimensions. This reformulation uses a very nice observation systematically made on a case by case basis in their work: a large class of internal (defect) boundary conditions preserving integrability is realised as Bäcklund transformations frozen at the point of the defect. I will review all these things (so everybody is welcome) and show how this can be recast in the efficient language of inverse scattering method, which will be introduced as well. Despite a possibly less appealing formalism (depending on your tastes), this approach has a number of advantages which I will present: unified proof of integrability for a large class of systems, explicit generating function of the integrals of motion, classification of defect conditions and finally, a possible way towards quantization. I will not talk about solitons, this topic having already been substantially covered by Ed and Peter.
• Thursday, 7 June 2007, 04:20 PM » 05:20 PM
Title: Poisson structures associated with the Schrödinger equation
Speaker: Ian Marshall
Room: G/109
Abstract: I shall present a new and surprisingly simple Poisson piece of the Schrödinger / KdV correspondence. It gives rise to a Poisson-Lie group of symmetries acting naturally on the space of wave functions.
• Monday, 11 June 2007, 04:20 PM » 05:20 PM
Title: Quasi-hermitian Liouville Theory
Speaker: University of Miami)
Room: G/109
Abstract: I will briefly discuss properties of quasi-hermitian (PT-symmetric) theories in the context of a simple exactly solvable example, "imaginary" Liouville theory. I will use a deformation quantization approach, i.e. QM in phase space. Then I will discuss the field theory extension of this model, of interest in string theory.
• Monday, 18 June 2007, 04:20 PM » 05:20 PM
Title: Expectation values for thermal states on lukewarm black holes
Speaker: Elizabeth Winstanley (University of Sheffield)
Room: G/109
Abstract: It is well-known that no regular "Hartle-Hawking"-like state can exist on Schwarzschild-de Sitter black holes, where the event and cosmological horizons are of different temperatures. However, for a Reissner-Nordstrom-de Sitter black hole where the two horizons have the same temperature ("lukewarm" black holes) then we may construct a regular thermal state at this temperature. We report on calculations of the renormalized expectation values of $\phi^2$ and $T_{\mu \nu}$ for this thermal state on a lukewarm black hole background. We follow the method of Anderson, Hiscock and Samuel, which will be reviewed in detail.

• Tuesday, 26 June 2007, 04:30 PM » 05:30 PM
Title: Enhanced black hole horizon fluctuations
Speaker: Larry Ford (Tufts University)
Room: G/020
• Thursday, 28 June 2007, 04:20 PM » 05:20 PM
Title: Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence. Lecture 1
Speaker: Alexander Chervov (Institute for Theoretical and Experimental Physics, Moscow)
Room: G/109
Abstract: The spectral curve is the key ingredient in the modern theory of classical integrable systems. We develop a construction of the "quantum spectral curve" and argue that it takes the analogous structural and unifying role on the quantum level also. In the simplest, but essential case the "quantum spectral curve" is given by the formula "det"$(L(z)-\partial_z)$ [Talalaev04] (hep-th/0404153). As an easy application of our constructions we obtain the following: quite a universal receipt to define quantum commuting hamiltonians from the classical ones, in particular an explicit description of a maximal commutative subalgebra in $U({\bf{gl}}_n[t])/t^N$ and in $U({\bf{gl}}_n[t^{-1}]) \otimes U(t\, {\bf{gl}}_n[t])$; its relation with the center on the of the affine algebra; an explicit formula for the center generators and a conjecture on W-algebra generators; a receipt to obtain the q-deformation of these results; the simple and explicit construction of the Langlands correspondence; the relation between the "quantum spectral curve" and the Knizhnik-Zamolodchikov equation; new generalizations of the KZ-equation; the conjecture on rationality of the solutions of the KZ-equation for special values of level. In the simplest cases we observe the coincidence of the "quantum spectral curve" and the so-called Baxter equation. Connection with the KZ-equation offers a new powerful way to construct the Baxter's Q-operator.
Based on hep-th/0604128 (authors: A. Chervov, D. Talalaev).
• Monday, 9 July 2007, 04:20 PM » 05:20 PM
Title: Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence. Lecture 2
Speaker: Alexander Chervov (Institute for Theoretical and Experimental Physics, Moscow)
Room: G/109
Abstract: The spectral curve is the key ingredient in the modern theory of classical integrable systems. We develop a construction of the "quantum spectral curve" and argue that it takes the analogous structural and unifying role on the quantum level also. In the simplest, but essential case the "quantum spectral curve" is given by the formula "det"$(L(z)-\partial_z)$ [Talalaev04] (hep-th/0404153). As an easy application of our constructions we obtain the following: quite a universal receipt to define quantum commuting hamiltonians from the classical ones, in particular an explicit description of a maximal commutative subalgebra in $U({\bf{gl}}_n[t])/t^N$ and in $U({\bf{gl}}_n[t^{-1}]) \otimes U(t\, {\bf{gl}}_n[t])$; its relation with the center on the of the affine algebra; an explicit formula for the center generators and a conjecture on W-algebra generators; a receipt to obtain the q-deformation of these results; the simple and explicit construction of the Langlands correspondence; the relation between the "quantum spectral curve" and the Knizhnik-Zamolodchikov equation; new generalizations of the KZ-equation; the conjecture on rationality of the solutions of the KZ-equation for special values of level. In the simplest cases we observe the coincidence of the "quantum spectral curve" and the so-called Baxter equation. Connection with the KZ-equation offers a new powerful way to construct the Baxter's Q-operator.
Based on hep-th/0604128 (authors: A. Chervov, D. Talalaev).
• Thursday, 12 July 2007, 04:20 PM » 05:20 PM
Title: Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence. Lecture 3
Speaker: Alexander Chervov (Institute for Theoretical and Experimental Physics, Moscow)
Room: G/109
Abstract: The spectral curve is the key ingredient in the modern theory of classical integrable systems. We develop a construction of the "quantum spectral curve" and argue that it takes the analogous structural and unifying role on the quantum level also. In the simplest, but essential case the "quantum spectral curve" is given by the formula "det"$(L(z)-\partial_z)$ [Talalaev04] (hep-th/0404153). As an easy application of our constructions we obtain the following: quite a universal receipt to define quantum commuting hamiltonians from the classical ones, in particular an explicit description of a maximal commutative subalgebra in $U({\bf{gl}}_n[t])/t^N$ and in $U({\bf{gl}}_n[t^{-1}]) \otimes U(t\, {\bf{gl}}_n[t])$; its relation with the center on the of the affine algebra; an explicit formula for the center generators and a conjecture on W-algebra generators; a receipt to obtain the q-deformation of these results; the simple and explicit construction of the Langlands correspondence; the relation between the "quantum spectral curve" and the Knizhnik-Zamolodchikov equation; new generalizations of the KZ-equation; the conjecture on rationality of the solutions of the KZ-equation for special values of level. In the simplest cases we observe the coincidence of the "quantum spectral curve" and the so-called Baxter equation. Connection with the KZ-equation offers a new powerful way to construct the Baxter's Q-operator.
Based on hep-th/0604128 (authors: A. Chervov, D. Talalaev).
• Thursday, 19 July 2007, 02:00 PM » 03:00 PM
Title: "Low Energy Quantum Gravity" workshop

All lectures will take place in B/B006 (Biology). The provisional program is below. For more details, see http://winstanley.staff.shef.ac.uk/LEQG.html

All are welcome to attend, but if you plan to attend, please send an e-mail to leqg.york@googlemail.com

Programme:

Low-Energy Quantum Gravity,

University of York, 19th-20th July 2007, Biology Lecture Theatre B/B006

Thursday 19th July

2.00 - 3.15 pm David Toms (Newcastle)

Quantum gravity and gauge coupling constants

3.15 - 3.45 pm Tea and coffee

3.45 - 4.25 pm Calvin Smith (Dublin)

Bounds on negative energy in quantum field theory

4.25 - 4.55 pm Jorma Louko (Nottingham)

How often does an accelerated particle detector click?

4.55 - 5.35 pm Jean Alexandre (KCL)

A non-perturbative time-dependent string configuration without extra dimensions?

Friday 20th July

9.30 - 10.45 am Karl-Henning Rehren (Gottingen)

AdS-CFT correspondence and CFT with boundaries

10.45 - 11.15 am Tea and coffee

11.15 am - 12.30 pm Remo Garattini (Bergamo)

A multi gravity approach to space-time foam

12.30 - 2.00 pm Lunch

2.00 - 2.40 pm Veronika Hubeny (Durham)

2.40 - 3.20 pm Atsushi Higuchi (York)

Infra-red properties of quantum field theories in de Sitter space-time

3.20 pm Tea and coffee

• Thursday, 26 July 2007, 04:20 PM » 05:05 PM
Title: Clustering and caustics in turbulent aerosols
Speaker: Michael Wilkinson (The Open University)
Room: G/109
Abstract:
Small particles suspended in a turbulent gas can cluster together.  It is widely believed that this is due to particles being  ‘centrifuged’ away from vortices. It has also been proposed that this clustering effect results in an increased rate of collision of particles.

I will describe recent results which quantify the clustering of particles, by means of a mapping to a perturbation of a nine-dimensional quantum harmonic oscillator. The centrifugal effect plays no role in my model, and the results are in good agreement with simulations of particles in turbulent flows.

I also argue that the increased rate of collision of particles in turbulent flows is primarily caused by the generation of caustics in the velocity field of the particles, rather than  spatial clustering.

These results are relevant to the initiation of rainfall from cumulus clouds, or the formation of planets from dust around  a young star.

# Spring 2007

The seminar takes place on Mondays and Thursdays: from 4:20 pm onwards in the very relaxed atmosphere of Room G/109 in Goodricke College. The seminars are preceded by tea from 4 pm. The typical length of the talks is about 1 hour.

• Monday, 15 January 2007, 04:20 PM » 05:20 PM
Title: Integrability and the AdS/CFT Correspondence
Speaker: Nick Dorey (DAMTP, Cambridge)
Room: G/109
Abstract: I will discuss the emergence of integrability in planar $N=4$ SUSY Yang-Mills and in the dual string theory on $AdS_{5} \times S^{5}$. I will also review recent progress in exploiting integrability to determine the exact spectrum.
• Thursday, 18 January 2007, 04:20 PM » 05:20 PM
Title: Spinor vector duality in fermionic $\mathbb{Z}_2 \times \mathbb{Z}_2$ heterotic-string orbifolds
Speaker: Alon Faraggi (University of Liverpool)
Room: G/109
• Monday, 22 January 2007, 04:20 PM » 05:20 PM
Title: Integrable systems, analytic difference equations, special functions, Hilbert space: On the crossroads
Speaker: Simon Ruijsenaars (Loughborough)
Room: G/109
Abstract: In this lecture we aim to survey the 4 areas mentioned above, with a bias towards the study of special classes of analytic difference operators. The problem of understanding their Hilbert space features centers around the issue of orthogonality and completeness of suitable eigenfunction transforms, which generalize various previously known transforms (the most well-known being Fourier transformation). The analytic difference operators arise from certain integrable systems, including nonlocal soliton equations and relativistic N-particle systems of Calogero-Moser and Toda type.
• Monday, 29 January 2007, 04:20 PM » 05:20 PM
Title: Reflection equation and twisted Yangians
Speaker: Andrey Mudrov (York)
Room: G/109
Abstract: With any involutive anti-algebra and coalgebra automorphism of a quasitriangular bialgebra we associate a reflection equation algebra. A Hopf algebraic treatment of the reflection equation of this type and its universal solution is given. Applications to the twisted Yangians are considered.
• Monday, 5 February 2007, 04:20 PM » 05:20 PM
Title: Black holes, qubits and the Fano Plane
Speaker: Michael Duff (Imperial College)
Room: G/109
Abstract: We review some recently established connections between the mathematics of black hole entropy in string theory and that of multipartite entanglement in quantum information theory. In the case of $N=2$ black holes and the entanglement of three qubits, the quartic $[SL(2)]^3$ invariant, Cayley's hyperdeterminant, provides both the black hole entropy and the measure of tripartite entanglement. In the case of $N=8$ black holes and the entanglement of seven qubits, the quartic $E_{7}$ invariant of Cartan provides both the black hole entropy and the measure of a particular tripartite entanglement encoded in the Fano plane.
• Monday, 12 February 2007, 04:20 PM » 05:20 PM
Title: Irreducibility of fusion modules over twisted Yangians at generic point
Speaker: Andrey Mudrov (York)
Room: G/109
Abstract: With any skew Young diagram one can associate a one parameter family of "elementary" modules over the Yangian $Y(gl_N)$. Consider the twisted Yangian $Y(g_N)$, a subalgebra in $Y(gl_N)$, associated with a classical matrix Lie subalgebra $g_N$ in $gl_N$. Regard the tensor product of elementary Yangian modules as multiparameter family of modules over $Y(g_N)$ by restriction. We prove irreducibility of such modules for generic values of the parameters.
• Monday, 19 February 2007, 04:15 PM » 05:15 PM
Title: Spin Foam models for quantum gravity
Speaker: John Barrett (Nottingham)
Room: G/109
• Thursday, 22 February 2007, 04:20 PM » 05:20 PM
Title: The $P(\Phi)_2$ model on the de Sitter space
Speaker: Christian Jaekel (University of Talca, Chile)
Room: G/109
This is joined work with J. Barata and J. Mund.
Abstract: We provide a self-contained construction of the model, based on a great variety of  methods and results from the literature, including harmonic analysis on symmetric spaces, group representation theory, Markov processes, Tomita-Takesaki modular theory and Osterwalder-Schrader reconstruction theorems. The thermal aspects (Hawking temperature) induced by the curvature and the exceptional case of  particles with small masses are discussed in the interacting case. We also explore the relations of the euclidean approach to the Wightman and Haag-Kastler axiomatic schemes which have been proposed for de Sitter space recently.
• Monday, 5 March 2007, 04:20 PM » 05:20 PM
Title: Vacuum Energy Density of a Quantized Scalar Field
Speaker: Stephen A. Fulling (Texas A&M University)
Room: G/109
Abstract: The energy density (as distinct from total energy) involves interesting mathematics and controversial physics. Regularization by an ultraviolet cutoff leads to reformulation of the problem in terms of "cylinder kernels" (Green functions of elliptic boundary value problems with an extra dimension), which can be related to heat and resolvent kernels, zeta functions, and local densities of states, but yield vacuum energies more directly. The signs of vacuum energies are related to the phases of oscillations in the eigenvalue density indexed by periodic orbits; for densities the relevant classical paths are closed but not necessarily periodic. The energy density generally is divergent as a boundary is approached, and therefore the naively renormalized total energy is not equal to the spatial integral of the renormalized density. This raises the issue of consistency of the theory with general relativity, as well as that of physical validity of calculations of Casimir forces other than those between rigid bodies. When the integration is done before the cutoff is removed, some of these divergences (notably those at corners) disappear. For the others we argue that the traditional renormalization philosophy is applicable: In the absence of a detailed microscopic model of the boundary material (playing the same role as unknown ultrahigh-energy physics), formally infinite terms should be replaced by finite terms with the same geometrical form and unknown coefficients that must be fixed experimentally. In particular, a consistent interpretation of the Einstein equation with distributional sources is being developed in collaboration with Ricardo Estrada, Kim Milton, Klaus Kirsten, and Lev Kaplan.
• Monday, 12 March 2007, 04:20 PM » 05:20 PM
Title: New methods in the study of non-equilibrium impurity systems: the interacting resonant level model
Speaker: Benjamin Doyon (Oxford)
Room: G/109
Abstract: With the example of the interacting resonant level model (IRLM), we show how to fully exploit simple properties of HershfieldÃ¢â‚¬â„¢s Y operator along with Ã¢â‚¬Å“impurity conditionsÃ¢â‚¬Â in impurity models in order to obtain perturbative expansions of quantum averages in any steady state. In non-equilibrium steady states, this offers a powerful alternative to Schwinger-Keldysh real-time perturbation theory or Lippmann-Schwinger scattering state formulation. We show how to solve the combinatorics of perturbative treatments, giving all integrals of the expansion without the use of Feynman diagrams. We also point out in this context how perturbation theory is connected to exact techniques based on Bethe ansatz. In the non-equilibrium IRLM, we obtain all integrals involved in the full perturbative expansion of the current in the Coulomb coupling U. Using renormalisation-group improvement, we obtain the current to first order in U for all values of voltage and temperature.
• Monday, 7 May 2007, 04:20 PM » 05:20 PM
Title: TBA
Speaker: Robert W. Spekkens (DAMTP, Cambridge)
Room: G/109

Please note that this is the tentative evolving program. It is advisable to (re-load and) re-check the page shortly before each talk. There is a mailing list for the seminar announcements. For further details please contact Boris Noyvert.

# Autumn 2006

The seminar takes place on Mondays and Thursdays: from 4:20 pm onwards in the very relaxed atmosphere of Room G/109 in Goodricke College. The seminars are preceded by tea from 4 pm. The typical length of the talks is about 1 hour.

• Monday, 9 October 2006, 04:20 PM » 05:20 PM
Title: Classical and Quantum Radiation Reaction
Speaker: Atsushi Higuchi (University of York)
Room: G/109
Abstract: In classical electrodynamics the self-force on a charged point particle due to its own electromagnetic radiation is described by the Lorentz-Dirac force.  We show that this force can be derived by taking the classical limit of the lowest-order perturbation theory in quantum electrodynamics. (This work was done in collaboration with Giles Martin.)
• Thursday, 19 October 2006, 04:20 PM » 05:20 PM
Title: CFT description of black holes
Speaker: Mukund Rangamani (Durham University)
Room:
G/109
• Monday, 30 October 2006, 04:20 PM » 05:20 PM
Title: Integrable defects
Speaker: Ed Corrigan (University of York)
Room: G/109
• Monday, 6 November 2006, 04:20 PM » 05:20 PM
Title: Form factors of XXX and XXZ mixed finite spin chains
Speaker: Olalla Castro-Alvaredo (City University London)
Room: G/109
Abstract: In this talk I will present new formulae for the form factors of the generators of the su(2) algebra associated to XXX quantum spin chains. The main novelty is that these formulae hold for generic spin representations of the operators considered, as well as for generic spin representations at the remaining sites of the chain. Therefore they can be specialized to a number of physically interesting cases such as alternating chains or spin chains with impurities. These expressions have been obtained by employing the approach developed by the group of the ENS-Lyon around J.-M. Maillet.
In addition, if I have enough time I will briefly describe how the so-called inverse scattering problem for the su(2)q spin generators characterizing the symmetry of quantum XXZ spin chains can be solved for generic spin representations.

• Thursday, 16 November 2006, 04:20 PM » 05:20 PM
Title: Defect lines in conformal field theory
Speaker: Ingo Runkel (King's College)
Room: G/109
Abstract: Just like one can define conformal boundary conditions for a two dimensional CFT, it is possible to join two CFTs along a conformally invariant "seam" or defect line. For such defects one can introduce reflection and transmission coefficients, defined via the stress tensors of the CFTs. Of particular interest are fully transmitting defects, because they contain information about symmetries and about order-disorder dualities of the CFT.
• Thursday, 23 November 2006, 04:20 PM » 05:20 PM
Title: Exact perturbation theory for Jacobi matrices
Speaker: Evgeny Sklyanin (University of York)
Room: G/109
Abstract: We report of the recent progress in developing an exact perturbative expansion for the spectrum and eigenvectors of tridiagonal (Jacobi) matrices. We present a new method of derivation of a multivariate hypergeometric representation for the series based on the multidimensional residue theory. A generalization to multiparameter spectral problem as well as possible applications to exactly solvable models (Bethe Ansatz) are discussed.
• Thursday, 30 November 2006, 04:20 PM » 05:20 PM
Title: Dynamical defects
Speaker: Peter Bowcock (Durham)
Room: G/109
• Thursday, 7 December 2006, 04:20 PM » 05:20 PM
Title: Associahedra and Integrable Models
Speaker: Charles Young (Durham university)
Room: G/109
Abstract: As part of some work in progress, Nicolas Crampe and I have found ourselves looking at interesting geometrical objects known as the "permutohedra", "associahedra", and even "permutoassociahedra". I will try to explain what these are and how they are related to integrable models and quantum groups.

# Spring 2006

The seminar takes place on Mondays and Thursdays: from 4:20 pm onwards in the very relaxed atmosphere of Room G/109 in Goodricke College. The seminars are preceded by tea from 4 pm. The typical length of the talks is about 1 hour.

Information on How to Reach the University is available. Goodricke College is building 24 on the campus map. Please contact Charles Young by e-mail if you need further information.

Please also check the Departmental Events Calendar for other seminars which might be of interest. For example the Departmental Colloquium talks on Wednesdays sometimes are on mathematical physics.

## Programme

Mon 9 January at 16:10:
Matt Leifer (Perimeter Institute)
Entanglement of overlapping systems and the breakdown of the tensor product

Mon 16 January at 16:10:
Yann Golanski (York)
Dark energy: Who would have thought Einstein was right?

Thu 26 January at 16:20:
Barry Miller (York)
Conserved charges of the principal chiral model on a supergroup

Mon 6 February at 16:20:
Oisin Mac Conamhna (Imperial College, London)
Classifying spacetimes with extended supersymmetry

Mon 13 February at 16:20:

Thu 16 February at 16:20:
Anna Lishman (Durham)
Identifying physical reflection factors using the exact g-function

Thu 23 February at 16:20:
Andreas Fring (City University, London)
Time evolution for non-Hermitian Hamiltonians

Mon 27 February at 16:20:
Supersymmetric heterotic string backgrounds.

Thu 2 March at 16:20:
Chong-Sun Chu (Durham)
Time dependent AdS/CFT and null singularities

Mon 6 March at 16:20:
Bernd Schroers (Herriot Watt)
Boundary terms in the Chern-Simons formulation of 2+1 gravity

Thu 9 March at 16:20:
Bogdan Stefanski (Imperial College)
Matching the gauge/string degrees of freedom in the large charge limit

Mon 13 March at 16:20:
Valya Khoze (Durham)
New results in the beta-deformed conformal N=4 SYM: Perturbative Amplitudes, AdS/CFT Correspondence...

# Autumn 2005

The seminar takes place on Mondays and Thursdays: from 4:20 pm onwards in the very relaxed atmosphere of Room G/109 in Goodricke College. The seminars are preceded by tea from 4 pm. The typical length of the talks is about 1 hour.

Information on How to Reach the University is available. Goodricke College is building 24 on the campus map. Please contact Charles Young by e-mail if you need further information.

Please also check the Departmental Events Calendar for other seminars which might be of interest. For example the Departmental Colloquium talks on Wednesdays sometimes are on mathematical physics.

## Programme

Please note that this is the tentative evolving program. It is advisable to (re-load and) re-check the page shortly before each talk. There is a mailing list for the seminar announcements. For further details please contact Charles Young

20th October 2005 Thursday 4.20pmDavid Kagan (DAMTP, Cambridge)
Supersymmetric Quantum Mechanics: Central Extensions and Extra Dimensions

24th October 2005 Monday 4.20pmMasashi Hamanaka (Nagoya University)
Towards Noncommutative Integrable Systems and Soliton Theories

27th October 2005
Thursday 4.20pm
Thomas Quella (Kings College, London)
Supergroup sigma-models and strings in RR backgrounds

31st October 2005
Monday 4.20pm
Mathematical Physics Group Meeting

3rd November 2005 Thursday 4.20pmCalvin Smith (York) TBA

7th November 2005 Monday 4.20pmBernard Kay (York)
Quantum Field Theory in Curved Spacetime

10th November 2005 Thursday 4.20pmTerry Rudolph (Imperial)
|How good must single photon sources be for optical quantum computation?+ |Loss tolerant cluster state computation

14th November 2005 Monday 4.20pm

17th November 2005 Thursday 4.20pmDavid Olive (Swansea)
Minimal representations and Freudenthal Triple Systems

21st November 2005 Monday 4.20pm

24th November 2005 Thursday 4.20pm

Valentina Riva (Oxford)
New perspective on critical phenomena: SLE and its connection with CFT.

28th November 2005 Monday 4.20pmRuth Williams (DAMTP, Cambridge)
Discrete Quantum Gravity

1st December 2005 Thursday 4.20pmGaetano Bertoldi (Swansea)
Large N double-scaling limits of 4d gauge theories

5th December 2005 Monday 4.20pm

8th December 2005 Thursday 4.20pmJonathan Halliwell (Imperial)
Emergent Classicality via Commuting Position and Momentum Operators

12th December 2005 Monday 4.20pm

15th December 2005 Thursday 4.20pmLutz Osterbrink (York)
Energy inequalities for the non-minimally coupled scalar field

19th December 2005 Monday 4.20pmYann Golanski (York)
Dark energy: Who would have thought Einstein was right?

# Mathematical Physics Seminars Summer 2005

The seminar takes place on Mondays and Thursdays: from 4:20 pm onwards in the very relaxed atmosphere of Room G/109 in Goodricke College. The seminars are preceded by tea from 4 pm. The typical length of the talks is about 1 hour.

Information on How to Reach the University is available. Goodricke College is building 24 on the campus map. Please contact Bernard Kay by e-mail if you need further information.

## Programme

Please note that this is the tentative evolving program. It is advisable to (re-load and) re-check the page shortly before each talk. There is a mailing list for the seminar announcements. For further details please contact Bernard Kay
 28th April 2005 Thursday 4.20pm V/123 Christian Micheletti (SISSA, Trieste) Elastic properties of proteins: characterization of the flexibility of proteins and of their functional movements Note unusual venue: VANBRUGH V/123 9th May 2005 Monday 4.20pm I.V. Komarov (St. Petersburg) Poisson maps and Lax pairs for the so(4) Kowalevski top 16th May 2005 Monday 4.20pm Anne C. Davis (DAMTP, Cambridge) Exploring Extra Dimensions Through Cosmology 23rd May 2005 Monday 4.20pm Tobias Osborne (Bristol) General Monogamy Inequality for Bipartite Qubit Entanglement 30th May 2005 Monday 4.20pm Atsushi Higuchi (York) Asymptotic Freedom (Instructional Lecture) 6th June 2005 Monday 4.20pm Da-jun Zhang (Shanghai) Solutions in Wronskian form to soliton equations 13th June 2005 Monday 4.20pm Paul Sutcliffe (Kent) Schrodinger-Chern-Simons vortex dynamics 28th June 2005 Tuesday (11.45am to 6pm) Note: Five Mathematical Physics Seminars in the North British Mathematical Physics Seminar today 30th August 2005 Tuesday 4.20pm Dmitri Lebedev (ITEP, Moscow) On a class of Representations of Quantum groups and Moduli space of Monopoles I 2nd September 2005 Friday 11.30am Dmitri Lebedev (ITEP, Moscow) On a class of Representations of Quantum groups and Moduli space of Monopoles II

# Mathematical Physics Seminars Spring 2005

The seminar takes place on Mondays and Thursdays: from 4:20 pm onwards in the very relaxed atmosphere of Room G/109 in Goodricke College. The seminars are preceded by tea from 4 pm. The typical length of the talks is about 1 hour.

Information on How to Reach the University is available. Goodricke College is building 24 on the campus map. Please contact Bernard Kay by e-mail if you need further information.

Please also check the Departmental Events Calendar for other seminars which might be of interest. For example the Departmental Colloquium talks on Wednesdays sometimes are on mathematical physics.

## Programme

Please note that this is the tentative evolving program. It is advisable to (re-load and) re-check the page shortly before each talk. There is a mailing list for the seminar announcements. For further details please contact Bernard Kay

 17th January 2005 Monday 4.20pm Vincent Caudrelier (LAPTH, Annecy) Impurity in integrable systems: tools, examples and physical consequences 20th January 2005 Thursday 4.20pm Andrei Mudrov (MPI, Bonn) Explicit equivariant quantization of semisimple conjugacy classes of simple matrix groups 27th January 2005 Thursday 4.20pm Nicola Pinamonti (Trento, Italy) Conformal symmetry breaking on Killing horizons 31st January 2005 Monday 4.20pm Jorma Louko (Nottingham) Spin and charges: Weapons of mass construction 10th February 2005 Thursday 4.20pm Zoltan Nagy (Cergy-Pontoise) Construction of commuting traces and spin chains using dynamical quadratic algebras 17th February 2005 Thursday 4.20pm Matthias Christandl (CQG, Cambridge) Uncertainty, monogamy, and implications for entanglement 21st February 2005 Monday 4.20pm Ian Hinder (Southampton) Stability in numerical relativity 24th February 2005 Thursday 4.20pm Nilanjana Datta (CQG, Cambridge) Perfect state transfer in quantum spin networks 28th February 2005 Monday 4.20pm Jie Xiao (Tsinghua University, Beijing) Quiver representations, Ringel-Hall algebras and quantum groups 7th March 2005 Monday 4.20pm Graeme Mitchison (CQG, Cambridge) The spectra of quantum states and their marginals: a group representation perspective 10th March 2005 Thursday 4.20pm Veronique Hussin (CRM, Montreal) Degeneracies of the energy spectrum of the Jaynes-Cummings model and coherent states 14th March 2005 Monday 4.20pm Valentina Riva (Oxford) Semiclassical methods in 2D QFT: spectra and finite-size effects

# PhysicsHinderabstract2005

Abstract of Talk

Stability in Numerical Relativity

by Ian Hinder (Southampton)

When solving the Einstein equations numerically, much emphasis is placed on the stability of the numerical scheme. For formulations of the time evolution equations which are second order in space, special care has to be taken in the definition of stability. I review our recent work in this area, as well as notions of well-posedness for the associated second order in space PDE systems.

# PhysicsMitchisonabstract2005

Abstract of Talk

The spectra of quantum states and their marginals: a group representation perspective.

by Graeme Mitchison (CQG, Cambridge)

I shall describe joint work with Matthias Christandl in which we investigated the "quantum marginal problem". Imagine that one is given a bipartite quantum state (a density matrix rho_AB). By tracing out each party, one obtains two marginal states (density matrices rho_A and rho_B). The spectra of the original state and its two marginals consitute a special triple, and we found a way to characterize such triples in terms of representations of the symmetric group.

# PhysicsNagyabstract2005

Abstract of Talk

Construction of commuting traces and spin chains using dynamical quadratic algebras.

by Zoltan Nagy (Cergy-Pointoise)

I will talk about dynamical extensions of quadratic quantum exchange algebras introduced by Freidel and Maillet and discuss their fusion and comodule structures. I will then show how these structures allow for building of commuting traces and spin chain type hamiltonians.

# Mathematical Physics Seminars Autumn 2004

The seminar takes place on Mondays and Thursdays: from 4:20 pm onwards in the very relaxed atmosphere of Room G/109 in Goodricke College. The seminars are preceded by tea from 4 pm. The typical length of the talks is about 1 hour.

Information on How to Reach the University is available. Goodricke College is building 24 on the campus map. Please contact Bernard Kay by e-mail if you need further information.

Please also check the Departmental Events Calendar for other seminars which might be of interest. For example the Departmental Colloquium talks on Wednesdays sometimes are on mathematical physics.

## Programme

Please note that this is the tentative evolving program. It is advisable to (re-load and) re-check the page shortly before each talk. There is a mailing list for the seminar announcements. For further details please contact Bernard Kay

 18th October Monday 4.20pm Mathematical Physics Group Meeting 25th October Monday 4.20pm Martin Speight (Leeds) Algebraic topology of the Skyrme configuration space 28th October Thursday 4.20pm Minitalks by Atsushi Higuchi, Barry Miller and Charles Young (York) 1st November Monday 4.20pm Minitalks by Calvin Smith, Giles Martin, and Varqa Abyaneh (York) 11th November Thursday 4.20pm Simon Ross (Durham) Time-dependent spacetimes in AdS/CFT 15th November Monday 4.20pm Nick Evans (Southampton) A gravitational dual description of chiral symmetry breaking 22nd November Monday 4.20pm Roberto Casadio (Bologna) Improved WKB analysis of cosmological perturbations 25 November Thursday 4.20pm Richard Szabo (Heriot Watt) 2D Yang-Mills theory and moduli spaces of holomorphic differentials 2nd December Thursday 4.20pm Nicolas Crampe' (York) Closed and open spin chain in any representation 6th December Monday 4.20pm Ron King (Southampton) Local equivalence of two-qubit states: a problem in invariant theory 13th December Monday 4.20pm Robert Weston (Heriot Watt) Transmitting defects in solvable lattice models

Abstract of Talk

Improved WKB analysis of cosmological perturbations

I present improved WKB-type approximations in order to study cosmological perturbations beyond the lowest order. The methods are based on functions which approximate the true perturbation modes over the complete range of the independent variable, including the turning point, and employ both a perturbative Green's function technique and an adiabatic expansion in order to compute higher order corrections. The methods are tested on the benchmark of power-law inflation: the next-to-leading order adiabatic expansion yields the amplitude of the power spectra with excellent accuracy, whereas the next-to-leading order with the perturbative Green's function method does not improve the leading order result significantly. In more general cases, either or both methods may be useful.

# PhysicsKingabstract2004

Abstract of Talk

Local equivalence of two-qubit states: a problem in invariant theory

by Ron King (Southampton)

Two-qubit states can be described in terms of a density matrix. To classify states up to local equivalence it is necessary to study invariants that are polynomial in the density matrix parameters. Here we tackle the problem of not just counting the number of linearly independent polynomial invariants of given degree, but also identifying a suitable basis that can be used to generate them all quite explicitly. This is a classical invariant theory problem involving the group U(16) and its restriction to a particular subgroup U(2)xU(2). A complete solution is provided, including en route a few surprises and some interesting syzygies.

# Mathematical Physics Seminars Summer 2004

The seminar takes place on Mondays and Thursdays: from 4:20 pm onwards in the very relaxed atmosphere of Room G/109 in Goodricke College. The seminars are preceded by tea from 4 pm. The typical length of the talks is about 1 hour.

Information on How to Reach the University is available. Goodricke College is building 24 on the campus map. Please contact Bernard Kay by e-mail if you need further information.

Please also check the Departmental Events Calendar for other seminars which might be of interest. For example the Departmental Colloquium talks on Wednesdays sometimes are on mathematical physics.

## Programme

Please note that this is the tentative evolving program. It is advisable to (re-load and) re-check the page shortly before each talk. There is a mailing list for the seminar announcements. For further details please contact Bernard Kay

 19 April Monday 4.20pm Yvette Fuentes-Guridi (Oxford) Holonomic quantum computation in the presence of decoherence 26th April Monday 4.20pm Ed Copeland (Sussex) Trying to understand the nature of dark energy in the Universe 13th May Thursday afternoon No Seminar But ... There are some interesting MMath presentations 17th May Monday 4.20pm Alan George (York) Coupling the massive Klein-Gordon field to a boundary oscillator 20th May Thursday 4.20pm Andreas Winter (Bristol) Generic aspects of quantum entanglement 24th May Monday 4.20pm Alan George (York) Coupling the massive Klein-Gordon field to a boundary oscillator (continued) 27th May Thursday 4.20pm Gabor Toth (Eotvos University, Budapest) On N=1 supersymmetric boundary bootstrap 17th June Thursday 4.20pm Stefan Antusch (Southampton) Neutrino Mass Models 28 June Monday 4.20pm Zoltan Bajnok (Eotvos University, Budapest) Semiclassical Sine-Gordon on the strip

# PhysicsFuentes-guridiabstract2004

Abstract of Talk

Holonomic quantum computation in the presence of decoherence

by Yvette Fuentes-Guridi (Oxford)

We investigate the effects of decoherence in the geometric evolution of states of a degenerate quantum system. This is done by generalizing the scheme for geometric phases in open systems to non-Abelian holonomies. The formalism is applied to estimate the errors produced by performing an universal set of holonomic quantum gates in the presence of an environment. We pinpoint the source of error in the scheme that must be corrected to achieve holonomic quantum computation completely robust to decoherence.

# PhysicsWinterabstract2004

Abstract of Talk

Generic aspects of quantum entanglement

by Andreas Winter (Bristol)

Probability theory has some insight to offer into the typical behaviour of states on large composite quantum systems. For example, because they are of measure zero in state space, product states are "never" seen when drawing a pure state uniformly at random. It may already come as a surprise that for large local dimension in a bipartite system the overwhelming majority of all pure states is in fact close to maximally entangled.

But even more is true: random subspaces of close to full dimension will with overwhelming probability contain only almost maximally entangled states. This implies that under a certain natural probability measure the generic mixed state will have almost maximal entanglement of formation. On the other hand, the distillability properties of these states can be shown to be very poor, both for EPR pairs and for secret key.

The techniques carry over to multiparty states, and offer a vision of "generic entanglement" as highly irreversible but potentially quite uniform - in contrast to the bewildering array of different types of entanglement in an exact classification. This is joint work with Patrick Hayden and Debbie Leung (Caltech).

# Mathematical Physics Seminars Spring 2004

The seminar takes place on Mondays and Thursdays: from 4:20 pm onwards in the very relaxed atmosphere of Room G/109 in Goodricke College. The seminars are preceded by tea from 4 pm. The typical length of the talks is about 1 hour.

Information on How to Reach the University is available. Goodricke College is building 24 on the campus map. Please contact Bernard Kay by e-mail if you need further information.

Please also check the Departmental Events Calendar for other seminars which might be of interest. For example the Departmental Colloquium talks on Wednesdays sometimes are on mathematical physics.

## Programme

Please note that this is the tentative evolving program. It is advisable to (re-load and) re-check the page shortly before each talk. There is a mailing list for the seminar announcements. For further details please contact Bernard Kay

 15th January Thursday 4.20pm Alexander Mikhailov (Leeds) Infinite dimensional automorphic Lie algebras 19th January Monday 4.20pm David McMullan (Plymouth) Charges in gauge theories 22nd January Thursday 4.20pm Bernard Kay (York) Quantum Field Theory in Curved Spacetime 1 26th January Monday 4.20pm Bernard Kay (York) Quantum Field Theory in Curved Spacetime 2 29th January Thursday 4.20pm Bernard Kay (York) Quantum Field Theory in Curved Spacetime 3 2nd February Monday 4.20pm Anne Taormina (Durham) Symmetries of string theory 5th February Thursday 4.20pm Atsushi Higuchi (York) Quantum Field Theory in Curved Spacetime 4 9th February Monday 4.20pm David Pearson (Hull) Spectral analysis of Schrodinger operators in Quantum Theory 12th February Thursday 4.20pm Atsushi Higuchi (York) Quantum Field Theory in Curved Spacetime 5 16th February Monday 4.20pm Tim Hollowood (Swansea) Integrability and gauge theories 19th February Thursday 4.20pm Atsushi Higuchi (York) Quantum Field Theory in Curved Spacetime 6 26th February Thursday 4.20pm Gary Gibbons (DAMTP, Cambridge) Consistent dimensional reductions from higher dimensional gravity and super gravity theories 1st March Monday 4.20pm Koenraad Audenaert (Bangor) There, and back again: Quantum theory and global optimisation 4th March Thursday 4.20pm Chris Fewster (York) Quantum Field Theory in Curved Spacetime 7 8th March Monday 4.20pm no seminar 11th March Thursday 4.15pm G/010 Adrian Ottewill (University College, Dublin) Quantum fields near rotating black holes Note different venue and slightly earlier start 15th March Monday 4.20pm Chris Fewster (York) Quantum Field Theory in Curved Spacetime 8 18th March Thursday 4.20pm Chris Fewster (York) Quantum Field Theory in Curved Spacetime 9

# PhysicsAudenaertabstract2004

Abstract of Talk

There, and Back Again: Quantum Theory and Global Optimisation

We consider a problem in quantum theory that can be formulated as an optimisation problem and present a global optimisation algorithm for solving it, the foundation of which relies in turn on a theorem from quantum theory. To wit, we consider the maximal output purity $\nu_q$ of a quantum channel as measured by Schatten $q$-norms, for integer $q$. This quantity is of fundamental importance in the study of quantum channel capacities in quantum information theory. To calculate $\nu_q$ one has to solve a non-convex optimisation problem that typically exhibits local optima. We show that this particular problem can be approximated to arbitrary precision by an eigenvalue problem over a larger matrix space, thereby circumventing the problem of local optima. The mathematical proof behind this algorithm relies on the Quantum de Finetti theorem, which is a theorem used in the study of the foundations of quantum theory.

We expect that the approach presented here can be generalised and will turn out to be applicable to a larger class of global optimisation problems. We also present some preliminary numerical results, showing that, at least for small problem sizes, the present approach is practically realisable.

# Mathematical Physics Seminars Autumn 2003

The seminar takes place on Mondays and Thursdays: from 4:20 pm onwards in the very relaxed atmosphere of Room G/109 in Goodricke College. The seminars are preceded by tea from 4 pm. The typical length of the talks is about 1 hour.

Information on How to Reach the University is available. Goodricke College is building 24 on the campus map. Please contact Bernard Kay by e-mail if you need further information.

Please also check the Departmental Events Calendar for other seminars which might be of interest. For example the Departmental Colloquium talks on Wednesdays sometimes are on mathematical physics.

## Programme

Please note that this is the tentative evolving program. It is advisable to (re-load and) re-check the page shortly before each talk. There is a mailing list for the seminar announcements. For further details please contact Bernard Kay

 22nd September Monday 2.15pm Jason Szulc (York) Inequalities for marginal probabilities, quantum and classical 13th October Monday 4.20pm Mathematical Physics Group Meeting 16th October Thursday 4.20pm Akihiro Ishibashi (DAMTP, Cambridge) On stability of higher dimensional static black holes 20th October Monday 4.20pm Dan Tovey (Sheffield) Searching for Supersymmetric Dark Matter at Boulby Mine 23-25 October ABC-KLM Meeting 23rd October Thursday 4.30pm Erika Andersson (Strathclyde) Generalised measurements in quantum mechanics Note unusual time and place: The venue for this talk is now Derwent College room D/056 (10 minutes' walk from Mathematics Department) because the talk will take place within the ABC-KLM Meeting (see link above) 27th October Monday 4.20pm Sean Hartnoll (DAMTP, Cambridge) Black hole instabilities, thermodynamics and duality 30th October Thursday 4.20pm Davide Fioravanti (York) An idea of universality in theories with a mass scale 3rd November Monday 4.20pm Werner Nahm (IAS, Dublin) Conformal Field Theory and an extended Bloch group 10th November Monday 4.20pm Tomihiro Harada (QMW, London) Self-similar solutions, critical behaviour and convergence to attractor in gravitational collapse 13th November Thursday 4.20pm Jiannis Pachos (Imperial College, London) Coherent evolutions in one and two dimensional optical lattices. 17th November Monday 4.20pm Niall MacKay (York) The Mathematics and Physics of Yangians 1 20th November Thursday 4.20pm Michael Melgaard (Uppsala) Spectral Theory of Schr"{o}dinger and Dirac Operators with External Magnetic Fields. Part II: Aharonov-Bohm magnetic fields and Lieb-Thirring inequalities. Note This is the second of two talks. The first (which is subtitled Part I: Eigenvalue Asymptotics ) will be at 11.15 am on Wednesday 19th November in G/109 in the GANT seminar series. But it will not be necessary to have gone to that talk to understand this one. 24th November Monday 4.20pm Niall MacKay (York) The Mathematics and Physics of Yangians 2 27th November Thursday 4.20pm Viv Kendon (Imperial College, London) Quantum versions of random walks for quantum computing 1st December Monday 4.20pm Charles Young (DAMTP, Cambridge) Local conserved charges in supersymmetric sigma models 4th December Thursday 4.20pm Niall MacKay (York) The Mathematics and Physics of Yangians 3 8th December Monday 4.20pm Niall MacKay (York) The Mathematics and Physics of Yangians 4 11th December Thursday 4.20pm Niall MacKay (York) The Mathematics and Physics of Yangians 5

# Network in Algebraic Geometry, Boundary Conformal Field Theory and Noncommutative Geometry

## 23 - 25 October, 2003

Network     Speakers     Participants     Programme     Directions     Accommodation     Contacts

The objective of this network is to bring together groups in the UK having a common goal in pursuing the deep connections between mathematics and physics, primarily algebraic geometry, operator algebras and quantum groups in pure mathematics and conformal field theory, string theory and statistical mechanics in mathematical and theoretical physics. For more information and details of past meetings see the network's webpage.

Speakers:

Participants:

The meeting is open to all. Please register with the local organiser to receive further information. There is no conference fee. Some funds are available to fund participants belonging to one of the network nodes.

as well as: Erika Andersson (Strathclyde), Zoltán Bajnok (d) (Budapest), Vasily Golyshev, Lászlo Palla (d) (Budapest), Aidan Schofield (d) (Bristol), Jakob Stix (d) (Bonn), Gábor Takács (d) (Budapest)

Programme:

We have booked Derwent Terrace Room from the morning of Thursday 23rd of October until the afternoon of Saturday 25th of October. This room will serve as our base room which we will use for tea, coffee and discussions while the talks will take place in nearby lecture rooms.

Thursday 23rd October

morning Gathering in Derwent Terrace Room Lunch Evgueni Sklyanin Separation of variables and related topics in room D/056 Zoltán Bajnok Boundary quantum field theories in room D/056 Erika Andersson: Generalised measurements in quantum mechanics in room D/056 Dinner in the Roger Kirk centre

Friday 24th October

8:30 am Breakfast in Wentworth College Peter West tba in room L/037 Alessio Corti and Vasily Golyshev in room D/056 Lunch Alice Rogers: Morse Theory on Phase Space in room C/A/101 Reidun Twarok: Mathematical virology in room D/016 Tea and Coffe in Derwent Coffee room Aidan Schofield: Noncommutative moduli of vector bundles in room D/016 Dinner in the "Go Down Restaurant"

Saturday 25th October

8:30 am Breakfast in Wentworth College Jakob Stix: Introduction to logarithmic Geometry in room C/A/101 Shahn Majid: Fock space representation for Anyons in room D/056 Lunch in Vanbrugh College

There will be breaks with refreshments between all talks.

Directions:

The meeting will take place mostly in Derwent College. This is building 23 on the campus map

When you arrive at York railway station you can either take bus no 4 to Heslington Hall (building 1 adjacent to Derwent College) or take a taxi and ask the driver to drop you at Derwent College. Alternatively, in case you have a lot of luggage and will be staying in Wenworth College, see below, you could take the taxi to Wentworth College and then walk to Derwent College from there (5 or 10 minutes walk across campus).

Accommodation:

The following participants will be staying in Wentworth College (arrival and departure dates in parentheses):

1. Zoltán Bajnok (23-26)
2. Edwin Beggs (23-25)
3. Roger Behrend (23-25)
4. Partha Chakraborty (23-25)
5. David Evans (23-25)
6. Jan Grabowski (23-25 twin room)
7. Daniel Hoyt (23-25 twin room)
8. Alexander Kasprzyk (23-25 twin room)
9. Shahn Majid (23-25)
10. Jasbir Nagi (23-25 twin room)
11. Lászlo Palla (23-26)
12. Alice Rogers (23-25)
13. Aidan Schofield (23-25)
14. Jakob Stix (23-25)
15. Gábor Takács (23-26)
16. Gerard Watts (23-25)
17. Katrin Wendland (23-25)
18. Peter West (23-24)
The following participants will be staying in Victoria Villa for the first night only before moving into Wentworth College:
1. Alexander Kasprzyk
2. Jasbir Nagi
3. Roger Behrend

Contacts:
For further information contact
Gustav W Delius (York) or David E Evans (Cardiff).

BACK TO ABC-KLM NETWORK             BACK TO MATHEMATICAL PHYSICS GROUP AT YORK

Abstract of Talk

Generalised measurements in quantum mechanics

In standard textbooks on quantum mechanics, a quantum measurement is usually described as a projection in the eigenbasis of the measured observable. This definition of projective (von Neumann) measurements is, however, too narrow. It does not allow us to describe all possible experimental measurement procedures. For example, we cannot accommodate joint measurements of non-commuting observables. Also, in a real experiment, with detector inefficiencies and other imperfections, what results is generally not a projective measurement on the original measured quantum system.

Generalised quantum measurements can describe any measurement that can be realised on a quantum system (provided that quantum mechanics holds). They are often called POM or POVM measurements, and are essentialy obtained by removing the requirement that the measurement operators have to be projectors. This talk will introduce generalised measurements and explain why they are useful. Generalised measurements have important applications for example in quantum communication theory, where one wants to know exactly what the optimal measurement strategy for a certain kind of signal is. They can also describe joint measurements of non- commuting observables, as well as real experimental situations with imperfect detectors.

Abstract of Talk

Self-similar solutions, critical behaviour and convergence to attractor in gravitational collapse

General relativity as well as Newtonian gravity admits self-similar solutions due to the scale-invariance. This talk reviews self-similar solutions and their relevance to gravitational collapse. In particular, our attention is mainly paid on the crucial role of self-similar solutions in the critical behavior and attraction in gravitational collapse. Implications to cosmic censorship are also discussed.

# PhysicsKendonabstract2003

Abstract of Talk

Quantum versions of random walks for quantum computing

by Viv Kendon (Imperial)

Will we be using a quantum computer for numerical simulations in the next decade? Quantum computing offers the potential for exponentially more efficient calculations than classical computers. But not for all problems, we know of a set that make use of a quantum version of Fourier Transforms for their speed up (including factoring large numbers) and one example using a quantum version of a random walk. Other classes of problems, such as searching an unsorted database, can have at most a quadratic speed up. And then there are all the difficulties of actually building a quantum computer... I will give an introductory overview of quantum computing, suitable for the non-specialist, in the course of which my own work on quantum versions of random walks will get a brief mention.

# PhysicsNahmabstract2003

Abstract of Talk

Conformal Field Theory and an extended Bloch group

by Werner Nahm (IAS, Dublin)

Integrable perturbations of conformal quantum field theories in two dimensions and invariants of hyperbolic manifolds are both described by an extension of the Bloch group, an object in algebraic K-theory. For the quantum field theories, the Bethe ansatz yields finite order elements in this group, which statisfy certain algebraic equations. Examples are provided by pairs of ADET diagrams, and in the case of two A-type diagrams all solutions of these equations are obtained.

# PhysicsPachosabstract2003

Abstract of Talk

Coherent evolutions in one and two dimensional optical lattices

by Jiannis Pachos (Imperial)

We consider the controlled manipulation of one dimensional bosonic or fermionic optical lattices, induced by tunnelling or collisions of the atoms within the lattice. As an application, we discuss the implementation of quantum computation where each atom provides one qubit. The resulting quantum register is robust against dephasing due to longitudinal lattice decoherence. Further studies concern one or two dimensional optical lattices and result in solid state models with new intriguing three body interactions.

# Mathematical Physics Seminars Summer 2003

The seminar takes place on Mondays and Thursdays: from 4:20 pm onwards in the very relaxed atmosphere of Room G/109 in Goodricke College. The seminars are preceded by coffee from 4 pm. The typical length of the talks is about 1 hour.

Information on How to Reach the University is available. Goodricke College is building 24 on the campus map. Please contact Clare Dunning by e-mail if you need further information.

Please also check the Departmental Events Calendar for other seminars which might be of interest. For example the Departmental Colloquium talks on W ednesdays sometimes are on mathematical physics.

## Programme

Please note that this is the tentative evolving program. It is advisable to re-check the page shortly before each talk. There is a mailing list for the seminar announcements. For further details please contact Clare Dunning

 28 AprilMonday 4.20pm José Miguel Figueroa y O'Farrill (Edinburgh) Plane wave limits in string and gauge theory 6 MayTuesday 11:30 amUnusual Time Mark Gould (Brisbane) Classification of unitary representations of simple Lie superalgebras 22nd May Thursday 4.20pm Evgueni Sklyanin (York) Q-operator and separation of variables for Jack polynomials 29th May Thursday 4.20pm Betti Hartmann (Durham) Monopoles and "hairy" black holes 2nd June Monday 4.20pm Valeria Del Prete (KCL) A theoretical model for population coding of mixed continuous and discrete stimuli: from the linear rise to the asymptotic regime. 5th June Thursday 4.20pm Chris Fewster (York) Stability of quantum systems at three scales 9th June Monday 4.20pm Cristina Zambon (York) Classically integrable field theories with boundary conditions 16th June Monday 4.20pm Andy Hone (UKC) Peakons, Poisson brackets and a functional equation. 19th June Thursday 4.20pm Hugh Jones (Imperial) PT symmetry versus Hermiticity in Quantum Mechanics and Quantum Field Theory 23rd June Monday 4.20pm Jorma Louko (Nottingham) Higher dimensional Einstein black holes and AdS/CFT conjecture 26th June Thursday 4.20pm Roger Behrend (Cardiff) Reflections on the Reflection Equation 7 JulyMonday 4.20pm Martin Halpern (Berkeley) Twisted Open Strings from Closed Strings: The WZW Orientation Orbifolds 22nd July Tuesday 4.15pm Christopher Fuchs (Bell Labs) What is the Difference between a Quantum Observer and a Weatherman? 25th July Friday 2.15pm Ruediger Schack (Royal Holloway) Compatible quantum state assignments 8th September Monday 2.15pm Rainer Verch (Max Planck Institute, Leipzig) Generally covariant quantum field theory and spin and statistics for quantum fields on manifolds 22nd September Monday 2.15pm Jason Szulc (York) Inequalities for marginal probabilities, quantum and classical

# Mathematical Physics Seminars Spring 2003

The seminar takes place on Mondays and Thursdays: from 4:20 pm onwards in the very relaxed atmosphere of Room G/109 in Goodricke College. The seminars are preceded by coffee and biscuits. The typical length of the talks is about 1 hour.

Information on How to Reach the University is available. Goodricke College is building 24 on the campus map. Please contact Gustav Delius by e-mail if you need further information.

Please also check the Departmental Events Calendar for other seminars which might be of interest. For example the Departmental Colloquium talks on Wednesdays sometimes are on mathematical physics.

## Programme

Please note that this is the tentative evolving program. It is advisable to re-check the page shortly before each talk. There is a mailing list for the seminar announcements. For further details please contact Dr. B.S. Kay or Dr. G.W. Delius.

 16 JanuaryThursday 4.20pm Sam Braunstein (Bangor) Entanglement in quantum information processing 20 JanuaryMonday 4.20pm Ed Corrigan (York) Graduate Lectures on String Theory 30 JanuaryThursday 4.20pm Ian Drummond (Cambridge) Bi-metric gravity - an alternative to dark matter 6 FebruaryThursday 4.20pm Jonathan Halliwell (Imperial) Decoherence: Some Recent Developments 27 FebruaryThursday 4.20pm Fay Dowker (QMW) A spontaneous collapse model on a lattice 6 MarchThursday 4.20pm Francesco Ravanini (Bologna) Excited Boundary Flows in the Tricritical Ising Model 13 MarchThursday 4.20pm Jon Links (Brisbane) Exactly solvable model for atomic-molecular Bose-Einstein condensates 17 MarchMonday 4.20pm Klaus Fredenhagen (Hamburg) Time as an observable in quantum mechanics 19 MarchWednesday 4.20pm Klaus Fredenhagen (Hamburg) Quantum field theory in curved spacetime 20 MarchThursday 4.20pm Klaus Fredenhagen (Hamburg) Quantum field theory on noncommutative spacetimes

# Mathematical Physics Seminars Spring 2003

## Abstracts

Fay Dowker (Imperial)
A spontaneous collapse model on a lattice

The spontaneous collapse models of Ghirardi, Rimini and Weber (GRW), Pearle and others represent a promising direction of research towards an observer independent theory of fundamental matter. These models were first proposed in a non-relativistic framework and since then much attention has focused on the search for appropriately relativistic models. This is not only important in its own right, but seems to be a prerequisite to any hope of applying collapse model ideas to quantum gravity.

I will present a simple collapse model for a field theory, defined on a $1+1$ null lattice. Being a lattice model, it doesn't enjoy exact Lorentz invariance and so it may be argued that it is not relativistic'' at all. However, it is not unreasonable to hope that Lorentz invariance will be attained in an appropriate continuum limit. Moreover, in the view of some workers, the aspect of spacetime that is fundamental and survives its encounter with its quantum nemesis is its causal structure and, further, that this fundamental causal structure is discrete. If one is looking for a development of quantum theory suited to such beliefs about quantum gravity, our model has many attractive features: it is discrete, there is a causal structure, and there is a local evolution rule tied to that causal structure. I will show that it is very local'' in construction, though it gives rise to non-local correlations (as expected by Bell's Theorem). I will also show that, despite the non-local correlations, external agents cannot use the field to send superluminal signals.

Exactly solvable model for atomic-molecular Bose-Einstein condensates
Abstract: The prospect of producing a Bose-Einstein condensate comprised of a coherent superposition of atomic and di-atomic molecular states has been considered theoretically for some years, but only recently been realised experimentally. A simple two mode model for this phenomenon will be presented which admits an exact solution through the algebraic Bethe ansatz. As a first step towards understanding the behaviour of the model, both an asymptotic and numerical analysis is conducted for a particular limit. From this the ground state properties, scaling behaviour and quantum dynamics are examined.

# Mathematical Physics Seminars Summer 2002

 22 AprilMonday 4.20pm Richard Woodard (University of Florida) A Non-Technical (Honest!) Description of the Problem of Quantum Gravity 2 MayThursday 4.20pm Patrick Dorey (Durham) Exact S-matrices for the q-state Potts models 6 MayMonday 4.20pm Gustav W Delius (York) Graduate Lectures on Solitons and Boundaries: Classical Soliton Solutions 9 MayThursday 4.20pm Theodora Ioannidou (Kent) Bogomolny Yang-Mills-Higgs Solutions in (2+1) anti-de Sitter Space 13 MayMonday 4.20pm Paul Sutcliffe (Kent) Solitons in the Heart 16 MayThursday 4.20pm Charis Anastopoulos (Utrecht) Quantum mechanical histories and interference phases 20 MayMonday 4.20pm Bernhard Baumgartner (Vienna) Order relations for sets and inequalities for entropies 21 MayTuesday 5.20pmNote special time and venue: V/123 LMS Hardy LectureAlexander ItsThe non-linear Schroedinger equation on the half-line and on the interval 27 MayMonday 4.20pm Stephen Siklos (DAMTP) Singularities and invariants in general relativity 30 MayThursday 4.20pm Hendryk Pfeiffer (DAMTP) Spin foam models in quantum gravity 6 JuneThursday 4.20pm S.M. Chitre (Tata Institute) The seismic sun and solar neutrinos 13 JuneThursday Meeting of the North British Mathematial Physics Seminar 17 JuneMonday 4.20pm Thomas Roman (Connecticut) Constraints on Spatial Distributions of Negative Energy 20 JuneThursday 4.20pm Tony Sudbery (York) Quantum Fallacies A guided discussion

# Mathematical Physics Seminars Spring 2002

 14 JanuaryMonday 4.20pm Jose Figueroa-O-Farrill (Edinburgh) Lie Branes: recent results 17 JanuaryThursday 4.20pm Larry Ford (Tufts) Focusing Vacuum Fluctuations 21 JanuaryMonday 4.20pm Katsushi Ito (Tokyo Institute of Technology) Scattering of noncommutative solitons 24 JanuaryThursday 4.20pm Kevin Graham (King's College, London) Perturbations of Conformal Field Theory by Boundary Condition Changing Operators 31 JanuaryThursday 4.20pm Atsushi Higuchi (York) Discussion on Topological K-Theory 4 FeburaryMonday 4.20pm Atsushi Higuchi (York) Discussion on Topological K-Theory 5 FebruaryTuesday 4.20pm(Note unusual day) Michael Atiyah (Edinburgh) K-theory and charges 7 FeburaryThursday 4.20pm Yann Golanski (NNDG York) Modelling of early stages of stellar formation 11 FebruaryMonday 4.20pm James Gray (Newcastle) Moving branes in Heterotic M-theory cosmology 14 FebruaryThursday 4.20pm Ian Lawrie (Leeds) Dissipation and friction in the equations of motion for scalar fields 18 FebruaryMonday 4.20pm David Toms (Newcastle) Quantum Fields off the Brane 21 FebruaryThursday 4.20pm Andrei Bytsko (Steklov Institute, St.Petersburg) Hamiltonians for higher spin XXZ chains 11 MarchMonday 4.20pm Robert Oeckl (Marseille) tba

# Mathematical Physics Seminars Autumn 2001

The seminar takes place on Mondays and Thursdays: from 4:20 pm onwards in the very relaxed atmosphere of Room V/131 in Vanbrugh College. The seminars are preceeded by coffee and biscuits. The typical length of the talks is about 1 hour. For further details please contact Dr. B.S. Kay or Dr. G.W. Delius.

 15 OctoberMonday 4.20pm Jason Szulc (York) The Nobel-prize-winning experiment on Bose-Einstein condensation 18 OctoberThursday 4.20pm Atsushi Higuchi (York) Low-frequency scalar absorption cross sections for stationary black holes 22 OctoberMonday 4.20pm Alan George (York) Quintessence 25 OctoberThursday 4.20pm Ruth Gregory (Durham) Braneworld instantons 29 OctoberMonday 4.20pm Mitch Pfenning (York) Radiation reaction in electromagnetism and general relativity: I electromagnetism 1 NovemberThursday 4.20pm Mitch Pfenning (York) Radiation reaction in electromagnetism and general relativity: II gravitation 5 NovemberMonday 4.20pm Chris Fewster (York) Microlocal Analysis This seminar forms part of the York Mathematics Department Series of expository seminars for staff and students 8 NovemberThursday 4.20pm Ian Jack (Liverpool) Finite non-commutative theories 12 NovemberMonday 4.20pm Tony Sudbery and Jason Szulc (York) Report on the Turin Meeting on Quantum Information (Note that the planned talks by Jochen Weller, previously announced in this slot, have had to be cancelled.) 15 NovemberThursday 4.20pm (no seminar) 19 NovemberMonday 4.20pm Ian McIntosh (York) A rough and ready guide to cohomology. Part 2: Cech cohomology This seminar forms part of the York Mathematics Department Series of expository seminars for staff and students 22 NovemberThursday 4.20pm Gustav Delius (York) Quantum group symmetry in the boundary sine-Gordon model and soliton reflection amplitudes 26 NovemberMonday 4.20pm John Loftin (Columbia) Toward a compactification of the moduli space of convex RP(2) surfaces 3 DecemberMonday 4.20pm Atsushi Higuchi (York) The renormalization group This seminar forms part of the York Mathematics Department Series of expository seminars for staff and students 10 DecemberMonday 4.20pm Chong-sun Chu (Durham) Aspects of noncommutative gauge theories 13 DecemberThursday 4.20pm Rafael Nepomechie (Miami) Supersymmetric integrable boundary QFT in 1+1 dimensions

# Mathematical Physics Seminars Summer 2001

Clicking on the highlighted dates in the calendar brings you to the seminar details in the programme below.
 April Mo Tu We Th Fr Sa So 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
 May Mo Tu We Th Fr Sa So 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
 June Mo Tu We Th Fr Sa So 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

## Times & Location

 Mondays & Thursdays: Talks start at 4:20 pm. They are preceeded by coffee and biscuits. The seminars are open ended but there will be a short break after about 50 minutes. They take place in the very relaxed atmosphere of Room V/131 in Vanbrugh College. Wednesdays: These are the Departmental Seminars and are supposed to be accessible to a general mathematics audience. They take place in room V/131, Vanbrugh College, at 4.00 pm. Tea will be available at 3.30 p.m. in the Senior Common Room, Vanbrugh College.

Information on How to Reach the University is available. Vanbrugh College is building 25 on the campus map. Please contact Gustav Delius by e-mail if you need a parking permit or would like further information.

## Programme

This term we will have lectures by Evgueni Sklyanin on selected topics in classical and quantum integrable models every Mondays starting on May 14.

Please note that this is the tentative evolving program. It is advisable to re-check the page shortly before each talk. For further details or to be placed on the mailing list please contact Dr. B.S. Kay or Dr. G.W. Delius.

 30 AprilMonday 4.20pm Dr Konstantina Savvidou (Imperial) Time in histories theory 3 MayThursday 4.20pm Dr Pascal Baseilhac (York) Expectation values of descendent fields in integrable quantum field theories 10 MayThursday 4.20pm Dr Anastasia Doikou (York) Principal chiral model scattering and the alternating quantum spin chain 16 MayWednesday 4.00pm Professor Paul Glendinning (UMIST) On the unique expansion of numbers in non-integer bases: a dynamical systems approach 17 MayThursday 4.20pm Dr Rod Crewther (Adelaide) Why I want Yang-Mills topological charge to take non-integer values 23 MayWednesday 4.00pm Dr Alan Beardon (Cambridge) Continued Fractions: Old and New 24 MayThursday 4.20pm Professor Rex Godby (York) Many-body perturbation theory for electrons in real materials 30 MayWednesday 4.00pm Dr Martin Matthieu (Queen's, Belfast) Elementary Operators on Calkin Algebras 31 MayThursday 4.20pm Dr Chris Fewster (York) Quantum Inequalities for the Dirac Field 6 Junespecial timeWednesday 4.20pm Ryu Sasaki (YITP, Kyoto University) Hierarchies of Spin Models related to Calogero-Moser Models (hep-th/0105197) 7 JuneThursday 4.20pm Daniel Vanzella (Sao Paulo) Decay of accelerated protons and the Fulling-Davies-Unruh effect 13 JuneWednesday 4.00pm Dr Julian Barbour The dynamics of pure shape 14 JuneThursday 4.20pm Dr Julian Barbour Relativity without Relativity 15 June special timeFriday 11.30am Dr Laszlo Feher (Szeged, Hungary) Interpretations and constructions of dynamical r-matrices 28 JuneThursday 4.20pm Professor Peter Holdsworth (ENS Lyon) Spin liquides glasses and ice: degeneracy and degeneracy lifting in frustrated magnetism 9 July special timeMonday 4.20pm Prof Larry Ford (Tufts) Where is the Negative Energy? - Constraints on Spatial Distributions of Negative Energy in Quantum Field Theory

# Classical and quantum integrable models: selected topics

## Lectures by E.K. Sklyanin

Mondays 4:20pm to 6pm, starting May 14.

### Abstract:

The lecture course covers a few advanced topics from the theory of integrable systems and is intended for the post-graduate and post-doctoral audience who is already familiar with the basics (definition of integrability according to Liouville-Arnold, Lax matrix, r-matrix, quantum group, Bethe Ansatz).

The topics include: Bäcklund transformations, Q-operator, separation of variables, integrable boundary conditions. The variety of techniques is illustrated on a few examples: Toda lattice, XXX magnetic chain, Calogero-Moser model.

### Detailed plan of lectures:

1. Integrability: a brief review of the basics
Liouville-Arnold's definition of integrability. Isospectral transform method: Lax matrix. Lie-Poisson groups: r-matrix. Symplectic leaves of r-matrix Poisson bracket. XXX magnetic chain as the generic integrable model associated to the sl2-invariant r-matrix. Degenerations of XXX model: DST model, Toda lattice, Gaudin model.

Quantization. Correspondence rules. Quantum canonical transformations: Fock formula. Quantum groups, Yangians. XXX magnetic chain, algebraic Bethe Ansatz.

2. Bäcklund transformations
Axioms of BT: algebraicity, locality, canonicity, commutativity (Veselov theorem), spectrality. General construction of BT for the models associated to the sl2-invariant r-matrix. Examples: Toda lattice, XXX chain, Calogero-Moser (Ruijsenaars) model.
3. Q-operator
History: motivations, Baxter's construction, Pasquier-Gaudin, Bazhanov-Lukianov-Zamolodchikov works. Relation of Q and BT.

Q-operator for the XXX model --- a detailed study. Universal sl2-invariant R-matrix. Q-operator as trace of a monodromy matrix. 3 kinds of Q-operators. Factorization of the R-matrix and the Q-operator. Fusion and wronskian identities. Kernels and symbols of Q.

4. Separation of variables
Definitions (classical and quantum case).

Classical SoV. General construction: poles of the eigenvectors of the Lax matrix. Normalization problem. Examples: Toda lattice, XXX model, Calogero-Moser model.

Relation of SoV and BT (Q). SoV from BT (Kuznetsov-Sklyanin). BT from SoV (Kuznetsov-Vanhaecke).

Quantum SoV. Examples: Toda lattice, XXX model, Macdonald polynomials.

5. Integrable boundary conditions
General construction based on exchange algebras. Comodules over quantum groups. Examples: XXX model, Toda lattice, Nonlinear Schröodinger equation.

Bethe Ansatz, SoV, Q-operator for the systems with boundary.

# Mathematical Physics Seminars Spring 2001

Clicking on the highlighted dates in the calendar brings you to the seminar details in the programme below.
 January Mo Tu We Th Fr Sa So 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
 February Mo Tu We Th Fr Sa So 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
 March Mo Tu We Th Fr Sa So 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

## Times & Location

 Mondays & Thursdays: Talks start at 4:20 pm. They are preceeded by coffee and biscuits. The seminars are open ended but there will be a short break after about 50 minutes. They take place in the very relaxed atmosphere of Room V/131 in Vanbrugh College (building 25 on campus map). Wednesdays: These are the Departmental Seminars and are supposed to be accessible to a general mathematics audience. They take place in room V/131, Vanbrugh College, at 4.00 pm. Tea will be available at 3.30 p.m. in the Senior Common Room, Vanbrugh College.
The seminar slots on Mondays and Thursdays which are not filled by a regular seminar talk will be used for the D-brane reading seminar.

## Programme

Please note that this is the tentative evolving program. It is advisable to re-check the page shortly before each talk. For further details or to be placed on the mailing list please contact Dr. B.S. Kay or Dr. G.W. Delius.

 11 JanuaryThursday 4.20pm Dr Roberto Tateo (Durham) Perturbed boundary conformal field theory and quantum mechanics 15 JanuaryMonday 4.20pm Spyros Kouris (York) Graviton two-point function in de Sitter space-time 18 JanuaryThursday 4.20pm Clare Dunning (York) Ordinary differential equations and integrable quantum field theories 22 JanuaryMonday 4.20pm Dr Keith Anguige Isotropic Cosmological Singularities 24 JanuaryWednesday 4 pm Dr Steven Bramwell (University College London) Universal Fluctuations in Correlated Systems 25 JanuaryThursday 4.20pm Professor Dmitri Vassiliev (Bath) Spectral asymptotics for partial differential operators and microlocal analysis 29 JanuaryMonday 4.20pm Jason Szulc (York) Shor's factorisation algorithm 31 JanuaryWednesday 4 pm Dr Benjamin Steinberg (Porto) What is partial symmetry? 1 FebruaryThursday 4.20pm Dr Davide Fioravanti (Durham) DE RERUM NATURA id est THE IMPORTANCE OF BEING SYMMETRY 7 FebruaryWednesday 4 pm Dr Paolo Papi (Rome) An overview on ad-nilpotent ideals of Borel subalgebras 8 FebruaryThurday 4.20pm Dr Andrew Mathas (Sydney) Affine Hecke algebras, Ariki-Koike algebras and Fock spaces 12 FebruaryMonday 4.20pm Dr Clifford Johnson (Durham) Gauge Theory Dynamics from D-Brane Probes 13 FebruaryTuesday 10.15pm Dr Evgueni Sklyanin (St. Petersburg) Note that this is not a regular seminar talk but a presentation in connection with the readership position in our group. 14 FebruaryWednesday 4 pm Professor J Greenlees (Sheffield) Implausible equivalences and duality 15 FebruaryThurday 4.20pm Dr Niall MacKay (York) Vibrations of symmetric molecules and the Buckyball 19 FebruaryMonday 4.20pm Professor Vladimir Rittenberg (Bonn) The two-component Burgers equation and applications to stochastic processes 21 FebruaryWednesday 4 pm Professor A Veselov (Loughborough) Configurations of hyperplanes in integrable systems 26 FebruaryMonday 4.20pm Dr Vadim Kuznetsov (Leeds) Bäcklund transformations go digital 28 FebruaryWednesday 4 pm Professor P Glendinning (UMIST) Postponed because of bad weather On the unique expansion of numbers in non-integer bases: a dynamical systems approach 7 MarchWednesday 4 pm Dr M Dritschel (Newcastle-on-Tyne) to be announced 7 MarchThursday 4 pm Professor Tony Sudbery (York) Groups, geometries and mechanics 12 MarchMonday 4.20pm Dr Konstantina Savvidou cancelled due to illness 22 MarchThursday 4.20pm Professor Tohru Eguchi (Tokyo) String propagation on singular Calabi-Yau manifolds

# Mathematical Physics Seminars Spring 2001

## Abstracts

Paolo Papi (Rome I)
An overview on ad-nilpotent ideals of Borel subalgebras
In a complex simple Lie algebra with a fixed Borel subalgebra b, an ad-nilpotent ideal is an ideal of b whose elements are ad-nilpotents. We will describe various approaches to the problem of encoding and enumerating such objects, with applications to representation theory and combinatorics.
Andrew Mathas (Sydney)
Affine Hecke algebras, Ariki-Koike algebras and Fock spaces
We describe the classification of the simple modules of the affine Hecke algebras of type A and the Ariki-Koike algebras. The key result is a deep result of Ariki's which builds upon work of Kazhdan, Lusztig and Ginzburg which connections the representation theory of these algebras with the representation theory of the quantum group of the affine special linear groups.
John Greenlees (Sheffield)
Implausible equivalences and duality
The talk arises from the idea that (fairly commutative) algebra is a branch of topology and that (fairly commutative) topology is a branch of algebra.

The aim is to give a framework in which the following phenomena can be treated simultaneously. However, the talk will only introduce a few of these examples and it should give a very concrete treatment.

1. Vector space duality
2. Poincar'e duality (of algebras, manifolds, ...)
3. Duality enjoyed by polynomial rings and by k[t^2,t^3] (for instance) but not by k[t^3,t^5,t^7]
4. Koszul duality (e.g. the correspondence between modules over Q[t] and modules over Q[t]/t^2).
5. classification of invariants of spaces with circle actions

Sasha Veselov (Loughborough)
Configurations of hyperplanes in integrable systems
The problem of classification of all integrable generalisations of the quantum Calogero-Moser system led to a new notion of the so-called locus configurations of hyperplanes. Such configurations turned out to be important for several other problems (for example, the classical Hadamard problem in the theory of Huygens' principle, the generalised WDVV equation). In the talk these configurations and the relevant results found by Berest, Chalykh, Feigin and the speaker will be discussed.

# Summer 2000

We have a seminar twice a week:

Days: Mondays and Thursdays talk at 4:15 pm, preceeded by coffee and biscuitsThe seminars are open ended but there will be a short break after about 50 minutes. Mondays in room G/010 in Goodricke College (building 22 on campus map), Thursdays in V/131 in Vanbrugh College (building 25 on campus map)

Other mathematical physics seminars take place in the Wednesday Departmental Seminar series and for convenience these too are listed in the programme below.

 Wednesday, 3 May: Departmental Seminar at 4:00 in V/131J-Y Thibou (Paris)Introduction to the Combinatorics of Ribbon Tableaux Thursday, 4 May: Niall MacKay (York)The Principal Chiral Model on the Half-Line Monday, 8 May: John Cardy (Oxford)Conformal Field Theory and Percolation Wednesday, 10 May: Departmental Seminar at 4.00 in V/131T Sapatinas (Kent)An introduction to wavelet decomposition and shrinkage Monday, 15 May: Francois Englert (Brussels)The Fefferman-Graham ambiguity and the holographic principle Wednesday, 17 May: Departmental Seminar at 4:30 in V/131Peter Phillips (Yale)Trends and Spurious Regression Monday, 22 May: Sergei Lukyanov (Rutgers)Finite temperature expectation values of local fields in the sinh-Gordon model Wednesday, 24 May: Departmental Seminar at 4:00 in V/131Fran Burstall (Bath)Integrable systems in Conformable Geometry Thursday, 25 May: Reidun Twarock (York)An aperiodic analog to the Virasoro algebra via quasicrystal techniques Wednesday, 31 May: Departmental Seminar at 4:00 in V/131Stephen Bramwall (University College London)Universal Fluctuations in Correlated Systems Wednesday, 7 June: Departmental Seminar at 4:00 in V/131Michael Berry (Bristol)The architecture of diffraction catastrophes Monday, 12 June: Peter Goddard (Cambridge)An approach to Conformal Field Theory Wednesday, 14 June: Departmental Seminar at 4:00 in V/131Paul Turner (Heriot-Watt)Homotopy Quantum Field Theories Thursday, 22 June: Don Marolf (Syracuse)String/M-Branes for relativists Thursday, 29 June: Tony Sudbery (York)Why Am I Me? and other interesting questions Monday, 3 July: Ryu Sasaki (Yukawa Institute, Kyoto)The Quantum Calogero-Moser Model Monday, 10 July: AM Semikhatov (Lebedev and Durham)Integrable Representations as Collective (Quasiparticle'') Excitations

# Spring 2000

We have two series of weekly Mathematical Physics seminars:

## Monday Seminars

Monday seminars take place at 4.15 in room G/010
 17 January: Chris Fewster  Quantum Inequalities from Microlocal Analysis 24 January: Liu Zhao  2-Parameter Deformations of Affine Lie Algebras 31 January: Pascal Baseilhac  From Reflection Amplitudes to Vacuum Expectation Values in Integrable Quantum Field Theories I 7 February: Spyros Kouris  Large Distance Behaviour of the Linearized Gravity Two-Point Function in De Sitter Spacetime 14 February: Ian McIntosh  Toda Systems and their Poisson Structures: the Co-adjoint Orbit Method I 21 February: Ian McIntosh  Toda Systems and their Poisson Structures: the Co-adjoint Orbit Method II 28 February: Ian McIntosh  Toda Systems and their Poisson Structures: the Co-adjoint Orbit Method III 6 March: Katrin Wendland (Bonn)  (Crystallographic) Orbifold Conformal Field Theories 13 March: Everyone  Informal Discussion on Quantum Gravity 20 March: Hilary Carteret (York)  {|Local Symmetry properties of three-particle pure states> + |Local Symmetry properties of multi-particle pure states>}/sqrt(2)

## Thursday Seminars

Thursday seminars take place at 4.15 in room V/131 (preceded by coffee at 4.00 in V/135).
 20 January: Jorma Louko (Nottingham)   Einstein-Kepler Problem in 2+1 Dimensions 27 January: Pascal Baseilhac (York)   Reflection Amplitudes of Non-Simply Laced Toda Theories and Thermodynamic Bethe Ansatz 3 February: Anastasia Doikou (Durham)   Solving the Bethe-Ansatz Equations 10 February: Everyone  Informal Discussion on Supersymmetric Quantum Mechanics 17 February: Nicolai Kitanine (York)   Correlation Functions in the XXZ Model 24 February: Everyone  Informal Discussion on Boundary Conformal Field Theory and String Theory 2 March: Malcolm Ludvigsen (York)  Timelike Infinity and the Final State of Black Holes 9 March: Tony Sudbery (York)  Entanglement 16 March: Chris Barton (York)  Magic Squares of Lie algebras

# Mathematical Physics Seminars Autumn 2000

Clicking on the highlighted dates in the calendar brings you to the seminar details in the programme below.
 October Mo Tu We Th Fr Sa So 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
 November Mo Tu We Th Fr Sa So 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
 December Mo Tu We Th Fr Sa So 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

## Times & Location

 Mondays & Thursdays: Talks start at 4:20 pm. They are preceeded by coffee and biscuits. The seminars are open ended but there will be a short break after about 50 minutes. They take place in the very relaxed atmosphere of Room V/131 in Vanbrugh College (building 25 on campus map). Wednesdays: These are the Departmental Seminars and are supposed to be accessible to a general mathematics audience. They take place in room V/131, Vanbrugh College, at 4.00 pm. Tea will be available at 3.30 p.m. in the Senior Common Room, Vanbrugh College.
The seminar slots on Mondays and Thursdays which are not filled by a regular seminar talk will be used for the D-brane reading seminar.

## Programme

Please note that this is the tentative evolving program. It is advisable to re-check the page shortly before each talk. For further details or to be placed on the mailing list please contact Dr. B.S. Kay or Dr. G.W. Delius.

 12 OctoberThursday 4.20pm Phil Isaac (Brisbane) Quantum Lie Algebras This will be a generally accessible talk about quantum groups and quantum Lie algebras 16 OctoberMonday 4.20pm Prof. John Roberts (Rome) Theory of Superselection Sectors 30 OctoberMonday 4.20pm Brett Gibson (York) Boundary Breathers in the sine-Gordon model on the half line 2 NovemberThursday 4.20pm Dr Dirk Kreimer (Mainz) From the combinatorics of Feynman diagrams to running physical parameters 8 NovemberWednesday 4pm Cancelled because of flooding:Dr M Dritschel (Newcastle-upon-Tyne) 9 NovemberThursday 5:15pmroom: V/045 Dr Chris Fewster (York) Open Lecture: A crash course in quantum mechanics This is part of a lecture series for non-scientists starting immediately after our usual seminar slot. 15 NovemberWednesday 4pm Dr Stephen Bramwall (University College London) Postponed because of flooding 16 NovemberThursday 4:20pm Dr Ruediger Schack (Royal Holloway) Postponed because of flooding 20 NovemberMonday 4:20pm Dr Lucien Hardy (C.Q.C. Oxford) Can quantum theory be obtained from reasonable axioms? 22 NovemberWednesday 4pm Professor P C Chatwin (Sheffield) Aspects of the only unsolved problem of classical physics 23 NovemberThursday 5:15pmroom: V/045 Dr Chris Fewster (York) Open Lecture: Neither here nor there but both: the central mystery of quantum mechanics This is part of a lecture series for non-scientists starting immediately after our usual seminar slot. 29 NovemberWednesday Yorkshire Differential Geometry Day 30 NovemberThursday 5:15pmV/045 Professor Tony Sudbery (York) Open Lecture: Putting weirdness to work: quantum information and quantum computing This is part of a lecture series for non-scientists starting immediately after our usual seminar slot. 4 DecemberMonday 4:20pm Dr Michael Roesgen (Bonn) Applications of (essential) paths in conformal field theory 6 DecemberWednesday 4pm Dr James Vickers (Southampton) How to multiply distributions 7 DecemberThursday 4:20pm Dr Ruediger Schack (Royal Holloway) Generalized measurements and quantum Bayes rule 11 DecemberMonday 4:20pm Dr David Rideout (Syracuse) A Stochastic Growth Dynamics for Causal Sets

# Mathematical Physics SeminarsAutumn 1999

We have two series of weekly Mathematical Physics seminars:
For further details or to be placed on the mailing list please contact Dr. B.S. Kay or Dr. G.W. Delius

## Monday Seminars

 25 October: 5-minute minitalks by F. Cornish, T. Brzezinski, E. Corrigan, G. Delius, C. Fewster, A. Higuchi, B. Kay, I. McIntosh, M. Nazarov, A. Sudbery. 1 November: Gustav Delius  Conformal Field Theory I 8 November: Tomasz Brzezinski  Algebraic Bethe Ansatz I 15 November: Gustav Delius  Conformal Field Theory II 22 November: Tomasz Brzezinski  Algebraic Bethe Ansatz II 29 November: Gustav Delius  Conformal Field Theory III 6 December: Ed Corrigan   The ADHM Construction I 13 December: Ed Corrigan   The ADHM Construction II

## Thursday Seminars

 21 October: Elizabeth Winstanley (Oxford)  Black holes, infinite hair and anti-de Sitter space 3 November: free discussions 11 November: Maxim Nazarov (York) Reflection equation and classical Lie algebras 18 November: Christopher Fewster (York)  A general quantum inequality 25 November: Tomasz Brzezinski (York) Algebraic Bethe Ansatz III: Solving the Bethe equations 2 December: Vadim Kuznetsov (Leeds)  Bäcklund transformations for classical and quantum integrable systems 9 December: Nicholas Dorey (Swansea) title tba

# Conformal Field Theory

I gave three introductory lectures on conformal field theory:

• In the first lecture I introduced complex coordinates and determined the two-point function of the free boson in 2-dimensional euclidean space as the simplest example of a conformal field theory.
• In the second lecture I introduced operators through the radial quantization procedure. We studied the energy momentum tensor of a free boson and derived the Virasoro algebra.
• In the third lecture (which was even less organised than the first two, sorry) we left the special example of the free boson and introduced the concept of primary conformal fields and their descendents. I indicated how correlation functions involving descendent fields are determined in terms of those of primary fields and finally I explained how the existence of null vectors in the Verma module generated by a primary field leads to differential equations for  the correlation functions of the primary field

Obviously I only scratched the surface. I recommend the following for further reading:

The links point to a local copy of the scanned versions of the papers stored at KEK.

Gustav W Delius, 29/11/99

# Publications

A full list of publications by all members of the Department is also available.

### 2008

Hawkins E.  2008.  Comm. Math. Phys.. 283:675–699.
.  2008.  Quantum Information and Computation. 8:0797-0818.
Corrigan E.  2008.  VII International Workshop Lie Theory and Its Applications in Physics Varna, 18-24 June 2007.
.  2008.  Nuclear Physics B. 804
.  2008.  Nuclear Physics B. 797
.  2008.  Phys. Rev. D. 78(8):084031.
Fewster CJ.  2008.  Lecture Note 39/2008 of the Max Planck Institute for Mathematics in the Natural Sciences.
.  2008.  Phys. Rev. A 78, 042312.
.  2008.  Physics Letters A. 372:4379-4380.
.  2008.  Phys. Rev. A 78, 020303(R).
.  2008.  Classical and Quantum Gravity. 25:225015:1-20.
.  2008.  J. Phys. A: Math. Theor.. 41:025402:1-19.
Fewster CJ.  2008.  The Eleventh Marcel Grossmann Meeting - Proceedings of the MG11 Meeting on General Relativity. :2683-2685.
.  2008.  Journal of Physics A. 41(45)
.  2008.  Nuclear Physics B. 797
.  2008.  Journal of Mathematical Physics. 49:032104/1-22.
.  2008.  Reviews of Modern Physics. 80:787-838.
Beneduci R.  2008.  IL NUOVO CIMENTO DELLA SOCIETÀ ITALIANA DI FISICA. B, GENERAL PHYSICS, RELATIVITY, ASTRONOMY AND MATHEMATICAL PHYSICS AND METHODS. 123

### 2007

.  2007.  JHEP. 09:099.

## Graduate Study in the Mathematical Physics Group

If you are fascinated by the mathematical beauty of physical theories, we invite you to apply to join our group as a graduate student and share our excitement.

If you would like to know how to apply for admission as a graduate student you should check out the main Mathematics PhD page where you can find a link to the online application form. There are various possibilities of funding including EPSRC, PPARC and University scholarships.

Once you are one of our graduate students you will benefit from the congenial atmosphere which characterizes our group.

You will choose one of our members of staff as your supervisor who guides your research work. In addition there will be two more members of staff who keep themselves informed about your research and who together make up your thesis advisory panel. You can find out more about the formal side of being a graduate student here on the departmental postgraduate study pages.

For you, more important than these formal arrangements will be the personal interactions within our group. You will have plenty of opportunity for informal conversations during our morning or afternoon coffee breaks. These take place at 11:00 and 16:00 in G/109, a room with Physics Seminarcomfortable chairs but also with a blackboard if you feel the urge to discuss research.

Twice a week, on Tuesday lunchtimes (1315) and Thursday afternoons (1615), we hold our very relaxed seminars in the cofffee room. We often have outside speakers on Thursdays but there remain plenty of free slots for local speakers and everyone can make suggestions for topics. The seminars are in the "Russian style", which means that the audience can interrupt the speaker with questions and often even longer discussions. It can happen that people from the audience come to the blackboard themselves to discuss a point. And the seminars are open ended; people simply leave when they have heard enough.

We do not run a formal MSc course, but we participate in the MAGIC network of video-conferenced graduate lectures. We also run local short series of lectures on topics of interest. For example, we have had short courses on conformal field theory, the algebraic Bethe Ansatz, string theory and D-branes, the ADHM construction, the coadjoint orbit method, Yangians, and quantum fields in curved spacetime.

Please take a look at the description of our research areas. One characteristic you will notice is that we stress that much of the beauty of physical theories lies in their mathematical details. We are not content with just the broad brushstrokes.

# PhD projects

## Integrable field theory

### Quantum and classical integrable field theory (Ed Corrigan)

Ed Corrigan has been investigating the properties of defects and boundaries in integrable (but not conformal) field theories with a view to classifying all possibilities. This is an extensive project with many facets. Some of the ideas and techniques are algebraic in flavour, others analytical, but most are novel and there are a number of areas suitable for development by a PhD student.

### Quantum integrability (Niall MacKay)

Niall MacKay works principally on algebraic aspects of quantum integrability, and is happy to supervise students on the hidden symmetry algebras (typically Yangians and other 'quantum groups') of integrable models, their representations and particle content. Most projects are suitable for students with an MSc-level background in theoretical physics (including strings, supersymmetry, QFT etc.), but some are more algebraic and may be suitable for pure mathematicians with an interest in mathematical physics. Past and current students have worked on: boundary scattering in AdS/CFT; the Yang-Baxter equation and invariant tensors of exceptional Lie groups; twist-deformed manifolds and cosmology; conserved charges in supergroup sigma models; boundary scattering in principal chiral models; quantum affine Toda solitons.

Niall has also recently developed an interest in the mathematical modelling of warfare, and has published papers on Lanchester theory, especially in its historical context. Possible research projects would be in this area and in the mathematical modelling of counter-insurgent warfare.

## Quantum field theory and quantum gravitation

### Rigorous quantum field theory (Henning Bostelmann)

Henning Bostelmann is interested in the mathematical foundations of physics; specifically, of relativistic quantum physics (quantum field theory). While quantum field theory is a well established topic since more than 50 years, its mathematically rigorous description, in particular of its non-perturbative aspects, is still largely incomplete. He analyses these questions using advanced methods of functional analysis (operator algebras).

Topics that he is working on, and has worked on, include: the short-distance scaling limit of quantum field theories; the relation between pointlike observables (quantum fields) and bounded observables in open regions; the covariant formulation of these for quantum theories on curved spacetime, i.e., in a gravitational background.

### Quantum Field theory in curved spacetimes (Chris Fewster)

Chris Fewster works on the mathematically rigorous formulation of quantum field theory in curved spacetimes (QFT in CST). In this theory, the propagation of the quantum fields is affected by the curvature of spacetime, but (usually) one neglects the "back-reaction" effect of the quantum fields on the spacetime. He has supervised seven PhD students in this area, with two main foci:

Quantum energy inequalities Unlike most classical forms of matter, quantum fields can have local energy densities that are negative. However, quantum field theory contains mechanisms (deeply connected to the uncertainty principle) that result in the energy density not being too negative on average. These mechanisms are expressed by results called Quantum Energy Inequalities (QEIs). Chris Fewster has supervised a number of PhD students on these questions. Simon Dawson (PhD 2006) investigated numerical QEIs and also produced the first closed-form expression for QEIs for the Dirac field in CST. Calvin Smith (PhD 2006) obtained the first "absolute" QEIs in CST, while Lutz Osterbrink (PhD 2007) found the first QEIs applicable to the nonminimally coupled scalar field. An introduction to QEIs and some of the related techniques can be found in Chris Fewster's lecture notes.

Locally covariant QFT Quantum field theory in Minkowski space depends in many ways on the high degree of spacetime symmetry. General curved spacetimes lack any symmetry at all, which makes it hard to prove general statements about general quantum field theories (as opposed to specific models). A major development was the introduction by Brunetti, Fredenhagen and Verch of a locally covariant formulation of QFT in CST based on techniques of category theory. Chris Fewster's former students Ko Sanders (PhD 2008), Matthew Ferguson (PhD 2013) and current student Benjamin Lang have worked on various aspects of locally covariant QFT, including the proof of a Reeh-Schlieder theorem and the formulation of the Dirac field (Sanders), the dynamical locality of the extension of scalar field theory to incorporate Wick polynomials (Ferguson), and an investigation of dynamical locality and related issues for electromagnetism (Lang).

Hadamard states Quantum field theory admits a very large space of states, most of which are unphysical. The class of Hadamard states is a well-studied set of physical states, which play an important role in QFT in CST. With Benjamin Lang, Chris Fewster has recently given a new construction of a class of Hadamard states for the Dirac field in certain spacetimes. A number of open questions remain in this area.

In addition, Chris Fewster is interested in other aspects of QFT in flat and curved spacetime. Recently, with David Hunt (PhD 2012) he studied the quantization of linearized gravity on background spacetimes solving the Einstein equations with cosmological constant, thus making contact with Atsushi Higuchi's work (see elsewhere on this page).

### Quantum field theory: semi-classical limit (Atsushi Higuchi)

Classical and quantum electrodynamics are very old subjects and have been studied extensively. However, it has not been clear how the former is obtained as a classical limit of the latter in radiation processes. Working with a student, Giles Martin (PhD, 2008), he established that the classical back-reaction force on a radiating charged particle can be obtained as the classical limit from quantum electrodynamics (QED). He and Phil Walker (PhD, 2011) have calculated a quantum correction to the classical Larmor formula for the energy emitted from an accelerated charged particle. He is planning to extend his work on the semi-classical approximation in quantum field theory to radiation processes in curved spacetime and also apply it to gravitational radiation.

### Quantum field theory in de Sitter spacetime (Atsushi Higuchi)

Quantum field theory in de Sitter spacetime, which is relevant to inflationary cosmology, is believed to solve various puzzles in the big-bang cosmology. Atsushi Higuchi has supervised four PhD students in this area. With Spyros Kouris (PhD, 2003) he worked on constructing the two-parameter family of covariant propagators for gravitational waves, which will be useful in studying the gravitational fluctuation in this spacetime. With Richard Weeks (PhD, 2005) he found that the long-distance quantum correlation of quantum gravitational fluctuation is weaker than some physicists have suspected. With Yen Cheong Lee (PhD, 2010) he demonstrated how the retarded Green’s function can be used in de Sitter spacetime – there had been some confusion about this in the literature – and started investigating interacting field theory in this spacetime. With Mir Faizal (PhD, 2011) he worked on some aspects of interacting quantum gauge theory and perturbative quantum gravity. He is planning to work further on various aspects of interacting quantum field theory in de Sitter spacetime in the next few years.

## Quantum Information and Foundations

### Quantum mechanics and quantum information (Stefan Weigert)

You will have the opportunity to investigate topics in non-relativistic quantum mechanics with Stefan Weigert. The problems he is interested in are often motivated by questions currently addressed in quantum information.

In recent years, the properties of so-called mutually unbiased bases have attracted considerable interest in the quantum information community. Expressing complementarity of variables in quantum mechanics, they naturally give rise to fundamental questions about finite quantum mechanical systems, i.e. quantum systems accomodating a finite number of states. Recent PhD projects in this field have been based on analytic, numerical and computer-aided calculations.

### Foundations of quantum theory and quantum information (Paul Busch)

Paul Busch's main research interest is the development of the operational tools of quantum measurement theory and their application to the solution of conceptual problems and the modeling of practical measurement schemes. One strand of current work is concerned with structural aspects of finite-dimensional quantum systems (qudits), specifically the search for measures of approximation and degrees of unsharpness of quantum observables. Possible topics for PhD projects include the question of the connection between approximate joint measurability and approximate quantum cloning and the implications of these and other quantum measurement limitations for quantum information processing. Another possible project area is that of relativistic quantum measurements (covariant collapse, localisation vs. causality).

### Quantum information theory and the connection to quantum foundations (Roger Colbeck)

Roger Colbeck works on quantum information theory and quantum foundations.  Within quantum information theory, he works on quantum cryptography and quantum random number generation and the use of quantum and relativistic protocols for secure computations.  He also works on new uncertainty relations formulated in terms of entropy.  Much of his work connects quantum information and the foundations of quantum theory, for example, he has done work on the question of whether the world is random, and whether there could be theories that improve on the predictions of quantum mechanics.  There are many exciting directions this work could go in, and prospective PhD students should indicate any preferences they may have on their application form.

This year there are several additional opportunities in York created by the York centre for Quantum Technologies and the Quantum Communications hub. See here for more information.

# Visitors

Visitors to the Mathematical Physics group

Visitor Home institution Visit dates Host
Dr Tommaso Gentile Istituto Nazionale di Fisica Nucleare, Italy April 8, 2014 - September 20, 2014 Professor Paul Busch
Dr Dan McNulty Department of Optics, Palacky University Olomouc, Czech Republic February 17, 2014 - March 14, 2014 Dr Stefan Weigert
Dr Leon Loveridge University of British Columbia, Department of Physics and Astronomy, Vancover, Canada January 13, 2014 - January 17, 2014 Professor Paul Busch
Dr Roberto Beneduci University of Calabria, Italy December 16, 2013 - December 20, 2013 Professor Paul Busch
Dr Guido Bacciagaluppi School of Divinity, History and Philosophy, University of Aberdeen October 17, 2013 - October 18, 2013 Professor Paul Busch
Dr Alexis Roa Aguirre Instituto de Física Teórica, UNESP, Brazil September 30, 2013 - September 30, 2014 Professor Ed Corrigan
Professor Lawrence Ford Tufts University, Massachusetts, USA June 9, 2013 - June 14, 2013 Professor Chris Fewster
Professor Thomas Roman Department of Mathematical Sciences, Central Connecticut Sate University, USA June 9, 2013 - June 20, 2013 Professor Chris Fewster
Professor Rainer Verch Universitaet Leipzig, Germany May 13, 2013 - May 18, 2013 Professor Chris Fewster
Dr Marcus Appleby Queen Mary, University of London May 6, 2013 - May 7, 2013 Professor Paul Busch
Professor Ingemar Bengtsson University of Stockholm, Sweden April 30, 2013 - May 8, 2013 Professor Paul Busch
Dr Teiko Heinosaari University of Turku, Finland February 3, 2013 - February 8, 2013 Professor Paul Busch
Dr Roberto Beneduci University of Calabria, Italy January 21, 2013 - February 2, 2013 Professor Paul Busch
Dr Roger Colbeck ETH Zurich, Switzerland October 29, 2012 - October 31, 2012 Professor Paul Busch
Dr Andrei Babichenko Weizmann Institute September 1, 2012 - March 31, 2013 Prof. Niall MacKay
Dr Yuan Li Shaanxi Normal University, People's Republic of China September 1, 2012 - August 31, 2013 Professor Paul Busch
Professor Lawrence Ford Tufts University, Massachusetts, USA June 11, 2012 - June 15, 2012 Professor Chris Fewster
Dr Jukka Kiukas University of Nottingham June 6, 2012 - June 7, 2012 Professor Paul Busch
Professor Tirthankar Bhattacharyya Indian Institute of Science, Bangalore October 11, 2011 - October 13, 2011 Professor Paul Busch
Dr Roberto Beneduci University of Calabria, Italy October 1, 2011 - July 31, 2012 Professor Paul Busch
Professor Takayuki Miyadera University of Kyoto, Japan September 9, 2011 - October 6, 2011 Professor Paul Busch
Professor Dipankar Home Bose Institute, Calcutta, India August 15, 2011 - August 17, 2011 Professor Paul Busch
Dr Teiko Heinosaari University of Turku, Finland July 25, 2011 - July 31, 2011 Professor Paul Busch
Professor Lawrence Ford Tufts University, Massachusetts, USA June 10, 2011 - June 20, 2011 Professor Chris Fewster
Professor Pekka Lahti University of Turku, Finland June 6, 2011 - June 12, 2011 Professor Paul Busch