Workshop LQP46
Workshop on Foundations and Constructive Aspects of Quantum Field Theory
We are happy to welcome you to the 46th edition of the series of workshops on local quantum physics.
Date: 2425 June 2022.
Place: FAU ErlangenNürnberg, Bismarckstrasse 1a
Organizers:
Ricardo Correa da Silva
Gandalf Lechner
If you have any questions regarding the workshop, please write to lqp46@math.fau.de.
Contents
Accommodation
Accommodation options can be found at www.erlangen.info/lqp46/. Since other events are going to take place concomitantly in the area, we recommend booking your accommodation in advance.
More details will be announced in due time.
Program (draft)
The event will take place at Bismarckstrasse 1a (not at Mathematics or Physics building).
Friday
14:00 
Welcome 

14:10 
KarlHermann Neeb 

14:55 
Vincenzo Morinelli 

Coffee Break 

16:05 
Christiane Klein 

16:40 
Bartosz Biadasiewicz 

Coffee Break 

17:40 
Edoardo D’Angelo 

18:15 
Conserved Charges for the sineGordon Model in perturbative Algebraic Quantum Field Theory 
Fabrizio Zanello 
~20:00 
Dinner 
Saturday
09:00 
Daniela Cadamuro 

09:45 
On the Relative Entropy on QFT in globally hyperbolic spacetimes 
Fabio Ciolli 
Coffee Break 

10:55 
Maximilian H. Ruep 

11:30 
Jan Mandrysch 

Lunch 

14:00 
Quantum Theories and their Classical Limit: a C*−Algebraic Approach 
Christiaan van de Ven 
14:45 
Ko Sanders 
Registration
Registration is still open. Please use the form below to register.
Registered Participants
Last updated on 16 May 2022
Valentino  Abram  Trento 
Bartosz  Biadasiewicz  Poznań 
Alberto  Bonicelli  Pavia 
Henning  Bostelmann  York 
Romeo  Brunetti  Trento 
Detlev  Buchholz  Göttingen 
Daniela  Cadamuro  Leipzig 
Adriano  Chialastri  Roma 
Fabio  Ciolli  Roma 
Ricardo  Correa da Silva  Erlangen 
Edoardo  D’Angelo  Genova 
Claudio  Dappiaggi  Pavia 
Tasarla  Deadman  Cardiff 
Felix  Finster  Regensburg 
Markus  Fröb  Leipzig 
Tiziano  Gaudio  Roma 
Kristina  Giesel  Erlangen 
Johannes  Große  Erlangen 
Muxin  Han  Florida 
Arne  Hofmann  Göttingen 
Azam  Jahandideh  Poznań 
Daan  Janssen  Leipzig 
Christiane  Klein  Leipzig 
Ian  Koot  Erlangen 
Janik  Kruse  Poznań 
Gandalf  Lechner  Erlangen 
Kang  Li  Erlangen 
Hongguang  Liu  Erlangen 
Jan  Mandrysch  Leipzig 
Catherine  Meusburger  Erlangen 
Yasmine  Mhirsi  Erlangen 
Christoph  Minz  Leipzig 
Ravi  Mistry  Brasilia 
Antonio Michele  Miti  Bonn 
Vincenzo  Morinelli  Roma 
Andrea  Moro  Trento 
KarlHermann  Neeb  Erlangen 
Jonas  Neuser  Erlangen 
Carlos I  Perez Sanchez  Heidelberg 
Claudia  Pinzari  Roma 
KarlHenning  Rehren  Göttingen 
Paolo  Rinaldi  Bonn 
Anniela Melissa  Rodriguez Zarate  Erlangen 
Bharath  Ron  Vienna 
Nicolai  Rothe  Wuppertal 
Maximilian H.  Ruep  York 
Hanno  Sahlmann  Erlangen 
Yafet  Sanchez Sanchez  Hannover 
Ko  Sanders  Dublin 
Leonardo  Sangaletti  Leipzig 
Gregor  Schaumann  Würzburg 
Robert  Schlesier  Leipzig 
Federico  Sclavi  Pavia 
Karim  Shedid Attifa  Leipzig 
Tobias  Simon  Erlangen 
Christiaan  van de Ven  Würzburg 
Berend  Visser  York 
Daniele  Volpe  Trento 
Fabrizio  Zanello  Göttingen 
Travel Instructions
From Nuremberg Airport one can easily achieve Erlangen’s main station by taking Bus 30, which stops just a few meters from the airport’s exit and has its final stop either at Arcaden (which is just two blocks from the city centre) or at the Bahnhofplatz (which is the city centre) depending on the time.
The event is at a walkable distance from Erlangen’s main station, but for those who may need a bus, we suggest by now Bus 290.
The following picture shows the building entrance.
Abstracts
The geometry of modular groups on local nets
KarlHermann Neeb
We consider a net of algebras of local observables on a manifold M on which a finitedimensional Lie group G acts by symmetries and fixes a common cyclic separating vector for the local algebras. We further assume that one of the modular groups obtained from the TomitaTakesaki Theorem is contained in G. This assumption has surprisingly strong structural consequences: the generator of the modular group is a socalled Euler element.
As Euler elements can be classified and are closely related to causal symmetric spaces, one can now start from Euler elements and construct natural causal Gmanifolds on which nets of local algebras can be constructed. We also characterize the domains (generalized wedge domains) for which the modular groups can be identified.
This is joint work with Gestur Olafsson (Baton Rouge) and Vincenzo Morinelli (Rome)
Modular operator for null plane algebras in free fields
Vincenzo Morinelli
Abstract: We consider the algebras generated by observables in quantum field theory localized in regions in the null plane, in particular null cut regions. For a scalar free field theory, we will show that the oneparticle structure can be decomposed into a continuous direct integral of lightlike fibres and the modular operator decomposes accordingly. For this model we also compute the relative entropy of null cut algebras with respect to the vacuum and some coherent states and discuss QNEC.
ArXiv:2107.00039, Joint work with Y. Tanimoto (Univ. Tor Vergata), and B. Wegener (Univ. Tor Vergata)
Construction of the Unruh state on Kerrde Sitter
Christiane Klein
The study of quantum fields on curved spacetimes can reveal interesting physical effects, such as Hawking radiation in black hole spacetimes. The derivation of these effects requires the choice of an adequate Hadamard states for the quantum field theory. For the scalar field in Schwarzschild spacetime, one possible choice is the Unruh state, which has been shown to be a good approximation for the state of a scalar quantum field arising in gravitational collapse. In this work, we show how the Unruh state can be generalized to scalar fields Kerrde Sitter spacetimes and prove the Hadamard property for this generalization.
Local normality of Infravacuum States
Bartosz Biadasiewicz
This talk concerns an infravacuum representation introduced by K. Kraus, L. Polley and G. Reents. It is not equivalent to the standard vacuum representation of a massless scalar free field on the Minkowski spacetime. But for subalgebras corresponding to measurements performed within double cones, restrictions of respective representations are quasiequivalent. This means that the representation is locally normal. We give a straightforward proof of this fact which is based on the ArakiYamagami criterion.
Using this result we extend a recent approach to superselection theory, based on relative normalizers and conjugate classes, to a relativistic setting. The talk is based on arXiv:2106.02032, to appear in Lett. Math. Phys.
Wetterich equation on Lorentzian manifolds
Edoardo D’Angelo
Abstract: The Wetterich equation governs the renormalization flow of the effective action under a scaling of an IR cutoff k. In this talk, I introduce a generalization of the Wetterich approach to scalar field theories in generic, Hadamard states on globally hyperbolic, Lorentzian spacetimes, using techniques developed in the perturbative Algebraic Quantum Field Theory framework. The main novel ingredient is the use of a local regulator, which preserves the local covariance and unitarity of the theory. As a proof of concept, I also briefly discuss the application of the theory to thermal states in Minkowski space and to the BunchDavies vacuum in de Sitter space.
Conserved Charges for the sineGordon Model in perturbative Algebraic Quantum Field Theory
Fabrizio Zanello
As an example of integrable system, the classical sineGordon model exhibits an infinite number of conserved quantities, which are moreover in involution with respect to the Peierls bracket. The goal of my PhD project is to understand to what extent this structure is preserved in the setting of perturbative algebraic quantum field theory, considering the expected appearance of anomalies for the corresponding quantum sineGordon model and in view of previous results on the convergence of the scattering matrix.
Relative entropy of coherent states on general CCR algebras
Daniela Cadamuro
In QFT the total entropy of a state is generically infinite, so one considers the relative entropy between two states with reference to a subalgebra of the observables, such as the von Neumann algebra associated with a double cone or a spacelike wedge. Such entropy can be computed using TomitaTakesaki modular theory.
In this talk, we study the relative entropy for a subalgebra of a generic CCR algebra between a general (possibly mixed) quasifree state and its coherent excitations, and give a formula for this entropy in terms of singleparticle modular data. We also investigate changes of the relative entropy along subalgebras arising from an increasing family of symplectic subspaces, and study lower estimates for the second derivative of the relative entropy along this family, which replace the usual notion of convexity of the entropy. Our main input is a regularity condition for the family of subspaces (“differential modular position”) which generalizes the notion of halfsided modular inclusions. Examples include thermal states for the conformal U(1)current.
On the Relative Entropy on QFT in globally hyperbolic spacetimes
Fabio Ciolli
Abstract: Is reviewed the interesting case that the computation of Araki relative entropy for QFT may be obtained from the classical theory on oneparticle space, through a formula due to Roberto Longo. Then applications to the KleinGordon field are discussed, both in Minkowski and in globally hyperbolic spacetimes. In this latter case the result is obtained by introducing peculiar regions that produce, under admissible Killing flows, halfsided modular inclusions of local von Neumann algebras.
Local and causal quantum operations in AQFT
Maximilian H. Ruep
Starting from the requirement that a theory shall describe “observables” and “operations”, I will analyse the structure of AQFTs, i.e., of nets of local unital *algebras. Haag and Kastler’s original interpretation of AQFTs was in terms of nets of local operations, i.e., every appropriately normalised element induces a quantum operation via its adjoint action. This view will be shown to be challenged by an investigation of signalling causality in a scenario due to Sorkin. Instead, I will show that putting the emphasis on regarding the Hermitian algebra elements as observables suggests that associated local and causal operations reasonably have a structure close to that of a timeorderable prefactorization algebra of Benini, Perin and Schenkel. For additive AQFTs I will give a concrete example of an associated net of local and causal operations that in particular contains the update maps derived from the measurement schemes of Fewster and Verch. Finally, I will argue that Buchholz and Fredenhagen’s C*approach may then be regarded as specifying a net of (pure) local and causal operations, followed by finding an associated AQFT generated by observables.
This talk is based in parts on work together with H. Bostelmann and C. J. Fewster.
Quantum energy inequalities in integrable QFT models
Jan Mandrysch
Abstract: Many results in general relativity rely crucially on classical energy conditions imposed on the stressenergy tensor. Quantum matter, however, violates these conditions since its energy density can become arbitrarily negative at a point. Nonetheless quantum matter should have some reminiscent notion of stability, which can be captured by the socalled quantum (weak) energy inequalities (QEIs), lower bounds of the smeared quantumstressenergy tensor. QEIs could be proven in many free quantum field theory (QFT) models on both flat and curved spacetimes. In interacting theories only few results exist. We are here presenting analytical results on QEIs in interacting integrable QFT models in 1+1 dimension, in particular a stateindependent QEI for the case of a constant Smatrix and for a class of models at 1particle level including the O(n)nonlinearsigma model.
Quantum Theories and their Classical Limit: a C*−Algebraic Approach
Christiaan van de Ven
Quantization refers to the passage from a classical to a corresponding quantum theory. This notion goes back to the time that the correct formalism of quantum mechanics was beginning to be discovered. The converse problem, called the classical limit of quantum theories, is considered as a much more difficult issue and forms an important question for various areas of modern mathematical physics. As opposed to most traditional methods where one typically aims to obtain quantum mechanics from classical methods, this talk is based on quantization (more precisely, deformation quantization) as the study of the possible correspondence between a given classical theory, defined by a Poisson algebra or a Poisson manifold and possibly a (classical) Hamiltonian, and a given quantum theory, mathematically expressed as a certain algebra of observables or a pure state space. On the basis of this understanding quantization and the classical limit are two sides of the same coin.
In this talk I will present these ideas, first by introducing a natural framework based on the theory of C*−algebraic deformation quantization. Subsequently, I will show how this relates to the classical limit of quantum theories. More precisely, the socalled quantization maps allow to take the limit for h̄ of a suitable sequence of algebraic states induced by h̄dependent eigenvectors of several quantum models, in which the sequence typically converges to a probability
measure on the pertinent phase space.
In addition, since this C*algebraic approach allows for both quantum and classical theories, it provides a convenient way to study the theoretical concept of spontaneous symmetry breaking (SSB) as an emergent phenomenon when passing from the quantum realm to the classical world by switching off a semiclassical parameter. This is illustrated with several physical models, e.g. Schrödinger operators and meanfield quantum spin systems.
Constructing “nice” separable states
Ko Sanders
Entanglement is ubiquitous in quantum field theory, as can be seen e.g. from the ReehSchlieder theorem. However, QFTs also admit separable states between any two spacelike separated regions. Such separable states are important: when we want to quantify the amount of entanglement in a state, we essentially compute a kind of “distance” to the “nearest” separable state.
Abstractly, the existence of separable states follows from the split property, which also shows that such states are normal. However, little more is known about such states, even for free scalar QFTs. E.g., can separable states be Hadamard and have a finite energy density?
In this talk we consider separable states of a massive free QFT in Minkowski space. We develop some new mathematical tools to construct separable states with as many of the following desirable properties as possible: quasifree, Hadamard, stationary, homogeneous and isotropic.