39th LQP Workshop
"Foundations and Constructive Aspects of QFT"

Name:
Affiliation:

Detlev Buchholz: Infrared problems. A survey of more recent progress

Infrared problems appear in the setting of quantum field theory with long range forces at various levels: by divergences in perturbation theory, the failure of ordinary scattering theory and the inapplicability of fundamental results of the axiomatic approach. Whereas the first two problems found well-established solutions, the general (model independent) understanding of basic features, such as the existence of charge conjugation and of particle statistics remained to be longstanding open problems. In this talk solutions are presented which are based on the insight that experimental limitations (the arrow of time) provide a natural Lorentz invariant infrared regularization. Based on it simple charges of electric type and their conjugates, the statistics of the corresponding sectors and their covariance and energetic properties can unambiguously be determined and classified. (Joint work with the late John E. Roberts)

Klaas Landsman: Idealizations in quantum physics: Earman's Principle

The following normative principle was expressed by the renowned philosopher of science John Earman in 2004: "While idealizations are useful and, perhaps, even essential to progress in physics, a sound principle of interpretation would seem to be that no effect can be counted as a genuine physical effect if it disappears when the idealizations are removed." Despite its obvious validity, it is remarkable how often idealizations violate these principles. For example, all rigorous theories of spontaneous symmetry breaking in quantum statistical mechanics and in quantum field theory strictly apply to infinite systems only, since ground states of finite quantum systems are typically unique (and hence symmetric), whilst thermal equilibrium states of such systems (i.e. KMS states) are even always unique. The "Swiss" approach to the measurement problem based on superselection rules (Jauch, Hepp, Emch) faces a similar problem. We show how to deal with this principle, using the operator-algebraic language familiar to the Local Quantum Physics community.

Eli Hawkins: The Star-product in Interacting AQFT

When the *-product is expressed relative to the time-ordered product, the properties of the Møller operators become clearer. This simplifies the perturbative computation of the interacting *-product. The result is a formula that makes sense nonperturbatively.

Maximilian Duell: Particle Interpretation of Wedge-Local Quantum Field Theories

I will present a construction of multi-particle scattering states which is suitable for a large class of wedge-local QFTs, including e.g. Grosse-Lechner-type models. A corresponding scattering theory up to the two-particle level has been developed previously, but a generalization to higher particle numbers was not expected for geometric reasons. Lifting this restriction allows us to formulate and discuss the question of asymptotic completeness in the wedge-local setting.

Federico Faldino: Stability properties of KMS states in perturbative algebraic quantum field theory

Recently Fredenhagen and Lindner have constructed an interacting KMS state for a massive scalar field theory over Minkowski Spacetime in the framework of perturbative algebraic quantum field theory. In this talk, based on a joint work with N. Drago and N. Pinamonti (ArXiv:[ 1609.01124 ]), we analize the stability properties of this state. In particular, we prove the validity of the return to equilibrium property when the interaction Lagrangian has compact spatial support. On the other hand, this property ceases to hold if the adiabatic limit is considered, so an equilibrium state under the adiabatic limit for a perturbative interacting theory evolved with the free dynamics does not converge to the free KMS state. Indeed, we show that its ergodic mean converges to a non-equilibrium steady state for the free theory.

Nicoló Drago: On the adiabatic limit of Hadamard states

We consider the adiabatic limit of Hadamard states for free quantum Klein-Gordon fields, when the background metric and the field mass are slowly varied from their initial to final values. If the Klein-Gordon field stays massive, we prove that the adiabatic limit of the initial vacuum state is the (final) vacuum state, by extending to the symplectic framework the adiabatic theorem of Avron-Seiler-Yaffe. In cases when only the field mass is varied, using an abstract version of the mode decomposition method we can also consider the case when the initial or final mass vanishes, and the initial state is either a thermal state or a more general Hadamard state.

Hanno Gottschalk: Convoluted Generalized White Noise Never has Positive Metric - An Application of Baumann's Criterion

It is proven that the relativistic quantum fields obtained from analytic continuation of convoluted generalized (Lévy type) noise fields have positive metric, if and only if the noise is Gaussian. This follows as an easy observation from a criterion by Baumann, based on the Dell'Antonio–Robinson–Greenberg theorem, for a relativistic quantum field in positive metric to be a free field. The talk is based on joint work with Sergio Albeverio.

Oliver Matte: A Bismut-Elworthy-Li type formula in non-relativistic QED

Together with Batu Güneysu and Jacob Schach Møller we recently studied stochastic differential equations associated with the standard model of non-relativistic quantum electrodynamics (QED). In this talk we discuss differentiability properties of the corresponding stochastic flow. Furthermore, we present a Bismut-Elworthy-Li type formula for the derivatives of the semi-group generated by the non-relativistic QED Hamiltonian revealing the smoothing properties of the semi-group. Finally, we explain how to prove the smoothness of an associated Fock space operator-valued semi-group kernel.

Jan Derezinski: Quadratic bosonic Hamiltonians and their renormalization--general theory and examples from QFT

I will discuss relations of linear symplectic dynamics and their quantum counterparts in the case of an infinite number of degrees of freedom. In particular, I will describe conditions guaranteeing the existence of the (possibly, renormalized) quantum Hamiltonian and the formulas for its "vacuum energy". If time permits, I will discuss some examples from local QFT, which illustrate various difficulties in defining quantum dynamics: 1) mass-dependent perturbation of neutral bosons (dynamics exists in Fock space but an infinite renormalization of the Wick ordered Hamiltonian is necessary); 2) charged bosons in an external electromagnetic field (dynamics does not exists in Fock space, however the vacuum energy after an infinite renormalization is well defined).

Dang Nguyen Viet: Spectrum of Morse gradient flows

We will start by explaining what we mean by spectrum of a dynamical system from the point of view of resonances in dynamical systems and show how this concept relates to the instantonic theories studied by Frenkel-Losev-Nekrasov. Then we describe some work in collaboration with Gabriel Rivière (Lille 1 university) where we calculate such spectras for generic gradient flows. If time permits, we shall give potential applications to topological field theories.

Daniela Cadamuro: Quantum backflow in scattering situations

Measurable quantities that have positive values in classical dynamical systems need not to be positive in quantum theory. For example, consider a free quantum mechanical particle in 1 dimension. There are quantum states in which the particle's velocity is positive with probability 1, but where the probability flux for its position is locally negative; that is, while its velocity points to the right, the particle travels to the left. These effects are however small and limited in space and time by certain lower bounds, which are called "quantum inequalities". Similar effects also appear for a particle whose motion is governed by a Schroedinger equation with a certain class of potentials. The talk will present some recent results and work in progress on this topic.

Thomas Norman Dam: The Spin-Boson model in the strong interaction limit

The Spin-Boson model is a model from QFT which describes a two level sys- tem coupled to a scalar field. In this talk, I will present new results about the strong interaction limit of the massive Spin-Boson model. As the interac- tion approaches infinity, one can under very general assumptions describe the asymptotics of the resolvent (in a suitable sense), the ground state energy and the ground state eigenvector. One application of these results is to show the existence of a non degenerate exited state in the strong interaction limit and prove that the energy of the excited state converges to the energy of the ground state. If time allows, I will also talk about why the results makes it hard to renormalise the Spin-Boson model and the strategy to prove the above mentioned results. This is joint work with Jacob Schach Møller.

Participants

Name	Affiliation
Dorothea Bahns	Mathematisches Institut, Universität Göttingen
Karsten Bohlen	Universität Wuppertal
João Braga de Góes e Vasconcellos	University of Genova
Detlev Buchholz	Universität Göttingen
Daniela Cadamuro	Universität Göttingen
Joachim Cuntz	WWU Münster
Jonas Dahlbæk	Aarhus University, Department of Mathematics
Thomas Norman Dam	Aarhus University
Jan Derezinski	University of Warsaw
Nicoló Drago	Genoa University
Maximilian Duell	Technische Universität München
Steven Duplij	Münster
Wojciech Dybalski	Technische Universität München
Siegfried Echterhoff	WWU Münster
Michał Eckstein	Jagiellonian University, Kraków
Federico Faldino	University of Genova
Francesco Fidaleo	Università Tor Vergata, Roma
Christian Fleischhack	Universität Paderborn
Klaus Fredenhagen	II. Institut für Theoretische Physik, Uni Hamburg
Alexander Frei	LMU/TU München
Hanno Gottschalk	Universität Wuppertal
Eli Hawkins	University of York
Michael Kiss	University of York
Klaas Landsman	Radboud Universiteit Nijmegen
Max Lewandowski	Universität Potsdam
Oliver Matte	Aarhus Universitet
Gernot Münster	WWU Münster
Dang Nguyen Viet	Institut Camille Jordan Lyon 1
Carlos Pérez Sánchez	WWU Münster
Karl-Henning Rehren	Universität Göttingen
Kasia Rejzner	University of York
David Sabonis	TU München / University of Copenhagen
Jan Schlemmer	WWU Münster
Devashish Singh	Department of Mathematics, University of Genova
Ruben Stienstra	Radboud University Nijmegen
Michael Stiller	II. Institut für Theoretische Physik, Uni Hamburg
Alexander Stottmeister	Università Tor Vergata, Roma
Rainer Verch	Universität Leipzig
Raimar Wulkenhaar	WWU Münster
Jins de Jong	WWU Münster

Organizers

Carlos Pérez Sánchez (c_pere03 [-AT-] uni-muenster.de)
Jan Schlemmer (Jan.Schlemmer [-AT-] math.uni-muenster.de)
Jins de Jong (jinsdejong [-AT-] hotmail.com)
Raimar Wulkenhaar (raimar [-AT-] math.uni-muenster.de)

Last updated: January 19, 2017