Workshop on "Quantum Field Theory: Infrared problems and constructive aspects"
Dates: October 8-9, 2015
- Vincent Beaud
- Detlev Buchholz
- Daniela Cadamuro
- Jérémy Faupin
- Harald Grosse
- Andrzej Herdegen
- Giovanni Morchio
- Jens Mund
- Nicola Pinamonti
- Kasia Rejzner
- Ko Sanders
- Yoh Tanimoto
Thursday 8.10. | Friday 9.10. | |
---|---|---|
09:30 - 10:15 | Buchholz | Grosse |
10:20 - 11:05 | Herdegen | Mund |
11:05 - 11:35 | Coffee break | Coffee break |
11:35 - 12:20 | Morchio | Sanders |
12:20 - 14:00 | Lunch | Lunch |
14:00 - 14:45 | Beaud | Cadamuro |
14:50 - 15:35 | Faupin | Tanimoto |
15:35 - 16:05 | Coffee break | Coffee break informal dicussions |
16:05 - 16:50 | Pinamonti | informal dicussions |
16:55 - 17:40 | Rejzner | |
19:00 | Conference dinner |
- Vincent Beaud: On the improper ground state of Nelson's massless model Slides
The translation invariant Nelson massless model is known to be a toy-model for the infrared problem arising in non-relativistic QED. Mathematically and in the one-particle sector, this manifests itself in the absence of a mass-shell at the bottom of the continuous energy-momentum spectrum. Construction of a ground state involves coherent non-Fock representations already known by Fröhlich and indexed by the total momentum of the system. Guided by the constructive proof of Pizzo, we present a simplified and somewhat subtly different proof of existence of such an improper ground state. This is joint work with G.M. Graf.
- Detlev Buchholz: The universal C*-algebra of the electromagnetic field Slides
A C*-algebra of the electromagnetic field is presented which is represented in any relativistic quantum field theory incorporating electromagnetism. It encodes basic features of the field such as Maxwell's equations, Poincaré covariance and Einstein causality. The dynamics of the field is fixed by (a) choosing some pure vacuum state in the dual space of the algebra and (b) proceeding to the quotient algebra with regard to the kernel of the corresponding GNS representation. This result serves to exemplify the close connection between the Haag-Kastler framework and conventional quantum field theory.
- Daniela Cadamuro: Wedge-local fields in integrable models with bound states Slides
In the context of constructive QFT in the operator-algebraic approach, wedge-local fields play an important role. After the work of Lechner to construct factorizing scattering matrix models with scalar S-matrices without bound states, we recently extended this construction to scalar S-matrices with poles in the physical strip (``bound states'') by exhibiting wedge-local fields which arise as a deformation of Lechner's fields with the so called ``bound state operator''. Similar techniques allow us to extend this construction to the Z(N)-Ising and the sine-Gordon models, namely models with a richer particle spectrum and which are believed to have bound states. In this talk I will present the construction of wedge-local fields in these models and future work to complete such construction.
- Jérémy Faupin: Spectral analysis of a model describing quantum friction Slides
We consider a quantum Hamiltonian model describing friction. The model represents a quantum particle interacting with a homogenous medium composed of independent, quantum scalar fields. The physical system is translation invariant, so that the Hamiltonian admits a direct integral decomposition with respect to the total momentum. We study the spectrum of the family H(p) of Hamiltonians at fixed total momenta p. In particular, we prove, under some infrared conditions, that H(p) has a unique ground state and that the rest of the spectrum of H(p) is purely absolutely continuous. This is joint work with S. De Bievre and B. Schubnel
- Harald Grosse: A solvable QFT in 4 dimensions Slides
We review our common work with Raimar Wulkenhaar: The regularization of a scalar field on Moyal space leads to a matrix model. All correlation functions are expressed in terms of the solution of a nonlinear integral equation. Taking a special limit leads to a 4 D QFT, which satisfies growth property, covariance and symmetry. We discuss the evidence for reflection positivity for the 2-point function, for a certain range of the coupling constant.
- Andrzej Herdegen: Tails are real
Long-range tails of infrared-singular fields are nonlocal, and as such are admitted a rather humble ontic status in standard local quantum field theory. We report on a programme aiming at giving them a higher position.
- Giovanni Morchio: Evidence for a modified LSZ condition and asymptotic field algebra in QED Slides
The problem of the construction of asymptotic charged fields in QED is examined in the light of a revisitation of Dollard's contributions to scattering theory. In general, a Dollard dynamics in shown to give rise to an asymptotic dynamics which is a group and to asymptotic fields which evolve according to it and can be obtained through modified LSZ formulas. In a space-time covariant model of QED, with heavy classical charged particles, asymptotic charged fields are obtained by a modification of the LSZ condition, represented by an electromagnetic string; they are canonical, but have non trivial, explicitly given, commutation relations with the asymptotic electromagnetic fields. On the scattering space, the total Hamiltonian is the sum of the free Hamiltonians of the asymptotic charged and photon fields; the absence of charged states with free energy-momentum relation follows from the commutation relations between asymptotic fields; the analogue of a mass shell appears in the Fourier transform of operators which also depend on the origin of the string.
- Jens Mund: An algebraic construction of interacting 2-dimensional models -- a program Slides
We present a programme for the construction of interacting models on 2-dimensional de Sitter space. It does not use fields (neither quantum nor classical), but only operator-algebraic concepts, in particular the Bisognano-Wichmann relation and relative Tomita-Takesaki theory. The idea is based on the observation that the P(phi) model on 2-dimensional de Sitter space can be formulated in such a way that for a fixed wedge region the interacting algebra coincides with the free one, and the interacting dynamics is the modular unitary group for this algebra and the interacting vacuum vector. Together with the free rotations this unitary group generates the interacting representation of the de Sitter group. The interacting model is then completely fixed by covariance and Haag duality (which implies that the algebras for smaller regions arise from taking intersections over wedge algebras). We conjecture that one can start with any vector in the free Hilbert space satisfying certain simple assumptions, and construct a representation of the de Sitter group as above from the modular group and the free rotations. This yields a covariant family of interacting wedge algebras. The non-triviality of the ensuing local algebras for smaller regions, however, seems to put more severe restrictions on the vector. We also comment on the possibility to construct models on Minkowski space by considering the limit of infinite radius (zero curvature) of de Sitter space.
- Nicola Pinamonti: The generalised principle of perturbative agreement and the thermal mass Slides
The Principle of Perturbative Agreement, as introduced by Hollands and Wald, is a renormalisation condition in quantum field theory on curved spacetimes. This principle states that the perturbative and exact constructions of a field theoretic model given by the sum of a free and an exactly tractable interaction Lagrangean should agree. During this talk we shall present an alternative proof of the validity of this principle in the case of scalar fields and quadratic interactions. In particular we shall show that, the composition of the inverse classical Möller map and the quantum Möller map is a contraction exponential of a particular type. Afterwards, we prove a generalisation of the Principle of Perturbative Agreement and show that considering a quadratic contribution of a general interaction either as part of the free theory or as part of the perturbation gives equivalent results. Motivated by the thermal mass idea, we use that obtained results to extend the construction of massive interacting thermal equilibrium states in Minkowski spacetime developed by Fredenhagen and Lindner to the massless case.
- Kasia Rejzner: Algebraic adiabatic limit in theories with local symmetries Slides
Recent advances in QFT on curved spacetimes caused a paradigm shift in the way the adiabatic limit is treated. I the absence of symmetries, the information we have at our disposal is the local information and taking the adiabatic limit has to be re-interpreted. On the algebraic level it is realized by taking an appropriate inductive limit of local algebras. However, the difficulty arises again on the level of states. These issues become particularly relevant in the context of theories with local symmetries, where the gauge invariance of the theory is possible only in the adiabatic limit.
- Ko Sanders: Modular Nuclearity: a generally covariant perspective Slides
Recent constructions of integrable QFT models have made essential use of a property of the ground state called modular nuclearity. This property is a modification of the (Hamiltonian) nuclearity property introduced by Buchholz and Wichmann, which is physically motivated by the idea that the phase space volume should not grow too rapidly with increasing energy, in order to admit a thermodynamic interpretation. In this talk, based on joint work (in progress) with Lechner, I argue that the definition of modular nuclearity can be extended to generally covariant theories (a la Brunetti-Fredenhagen-Verch) and that it has some nice properties: it is preserved under pull-backs and it behaves well under spacetime deformation. In addition I discuss the progress in verifying the modular nuclearity of all quasi-free Hadamard states of a free scalar field in any globally hyperbolic spacetime. Previous investigations already established it for the Minkowski vacuum.
- Yoh Tanimoto: Bound state operators in integrable QFT with bound states Slides
We aim at constructing observables in wedge regions for a class of two-dimensional quantum field theories. In these models, the particle number is preserved under the scattering process, yet the poles in the S-matrix should correspond to bound states of elementary particles. Our candidate operators for wedge-observables have curious domain properties. We argue that finding their right self-adjoint extensions will lead to the existence of Haag-Kastler nets for the models.
The workshop will take place at the Zentrum Mathematik of the TU München (Garching campus, metro stop "Garching-Forschungszentrum" U6) in room MI 03.10.011.Directions The map shows the position of the venue.
We kindly ask the speakers to take care of their hotel reservations. We recommend Hotel Antares ^{} in Munich and Hotel Hoyacker Hof ^{} in Garching due to convenient public transport connection and special rates for the guests of the faculty of mathematics by using the keyword QFT-Workshop. We suggest that you make a reservation as early as possible, since last minute lodging costs may be very high in Munich. In case of any problems with hotel reservations, do not hesitate to contact us. Löwenbräu Keller ^{} We thank Technische Universität München and Deutsche Forschungsgemeinschaft for financial support.
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