Workshop LQP49 (2024)
Workshop on Foundations and Constructive Aspects of Quantum Field Theory
We are happy to welcome you to the 49th edition of Local Quantum Physics Workshop Series in Erlangen.
Dates: 7-9 November 2024
Topics: This workshop is dedicated to mathematical quantum physics and more specifically quantum field theory. The topics covered here will hence be concentrated on quantum field theory (on Minkowski space or curved spacetimes, axiomatic, constructive, rigorous, Euclidean versions), as well as more general mathematical quantum physics, operator algebras (in particular, von Neumann algebras and subfactors), quantum information theory, and noncommutative geometry.
Venue: Mathematics Department, FAU Erlangen, Cauerstraße 11, lecture hall H13. This is in the south of Erlangen.
Accommodation:
Please book accommodation yourself. Some options can be found at www.erlangen.info/lqp49/ and are reserved until the 28th of October. You are also free to look for accommodation independently.
Organisers: LQP49 will be run by the LQP@FAU team. This will involve
Ricardo Correa da Silva
Johannes Große
Ian Koot
Gandalf Lechner
Contact: If you want to get notified about news regarding this event, please check this website that will be updated continuously with information on travel, location, funding, schedule, etc. If you have any questions, please write to lqp49@math.fau.de.
Program
Thursday
| 13:30-14:00 | Registration and Welcome | |
| 14:00-14:50 | Rainer Verch (Leipzig) | Quantum Non-Causality in Spacetime May Be Not Exclusively Quantum |
| 14:50-15:30 | Jan Mandrysch (Vienna) | Implementing a Causal Measurement Scheme for Quantum Fields |
| Coffee break | ||
| 16:00-16:40 | Beatrice Costeri (Pavia) | Trace anomaly for the Stress-Energy Tensor of a Self-interacting Scalar field on a curved spacetime |
| 16:40-17:20 | Albert Much (Leipzig) | Deformation Quantization of QFTs in curved spacetimes |
| 17:20-18:00 | Christoph Richter (Leipzig) | Scaling Limit of de Sitter Quantum Field Theories |
Friday
| 09:30-10:20 | Jan Derezinski (Warsaw) | Lamb shift as a problem in mathematical physics |
| 10:20-11:00 | Arne Hofmann (Hannover) | Casimir effect for dielectric media |
| Coffee break | ||
| 11:20-12:00 | Ian Koot (Erlangen) | Thermal Field theories and Wedge-Modular Inclusions |
| 12:00-12:40 | Markus Fröb (Leipzig) | New modular Hamiltonians |
| Lunch | ||
| 14:00-14:40 | Leonardo Sangaletti (Leipzig) | An L4 quantum energy inequality for the thermal sector |
| 14:40-15:20 | Jani Kastikainen (Würzburg) | Driven conformal field theory and circuit complexity |
| Coffee break | ||
| 15:50-16:30 | Andrea Pizzamiglio and Lorenzo Trezzini (Pavia) | Quantum Cellular Automata and their Classification |
| 19:00 | Dinner | |
Saturday
| 09:30-10:10 | Filippo Nava (York) | Interplay between boundary conditions and the Lorentzian Wetterich equation |
| 10:10-10:50 | Andras Laszlo (Budapest) | On the running and the UV limit of Wilsonian renormalization group flows |
| Coffee break | ||
| 11:10-11:50 | Maria Stella Adamo (Erlangen) | Osterwalder-Schrader axioms for unitary full VOAs |
| 11:50-12:40 | Sebastiano Carpi (Rome) | Vertex algebras and non-unitary Wightman CFTs |
Registered Participants
Last updated on the 24th of October 2024
| Maria Stella | Adamo | Friedrich-Alexander-Universität |
| Lea | Bossmann | Friedrich-Alexander-Universität |
| Daniel | Burgarth | Friedrich-Alexander-Universität |
| Sebastiano | Carpi | Università degli Studi di Roma Tor Vergata |
| Ricardo | Correa da Silva | Friedrich-Alexander-Universität |
| Beatrice | Costeri | Università di Pavia |
| Thomas | Creutzig | Friedrich-Alexander-Universität |
| Claudio | Dappiaggi | Università di Pavia |
| Christoph | Dehne | HEG ZM |
| Jan | Dereziński | University of Warsaw |
| Philipp | Dorau | Universität Leipzig |
| Carmine Alfonso | Ferrentino | University of Leipzig |
| Renata | Ferrero | Friedrich-Alexander-Universität |
| Christian | Fleischhack | Universität Paderborn |
| Gerardo Martin | Franco Cordova | Friedrich-Alexander-Universität |
| Markus B. | Fröb | ITP, Universität Leipzig |
| Stefano | Galanda | University of Genova |
| Luca | Giorgetti | University of Rome Tor Vergata |
| Johannes | Große | Friedrich-Alexander-Universität |
| Sidnei | Guerino Fabris Junior | Universidade Federal do Paraná |
| Arne | Hofmann | Leibniz-Universität Hannover |
| Tobias | Iding | Friedrich-Alexander-Universität |
| Jani | Kastikainen | University of Würzburg |
| Lars | Koekenbier | Friedrich-Alexander-Universität |
| Ian | Koot | Friedrich-Alexander-Universität |
| Alexander | Kulyabin | Friedrich-Alexander-Universität |
| Andras | Laszlo | HUN-REN Wigner Research Centre for Physics, Budapest |
| Latevi | Lawson | Max Planck Institute for the Sciences of Light |
| Gandalf | Lechner | Friedrich-Alexander-Universität |
| Kang | Li | Friedrich-Alexander-Universität |
| Hongguang | Liu | Friedrich-Alexander-Universität |
| Jan | Mandrysch | IQOQI Vienna |
| Victor Hugo | Marques Ramos | Universidade de São Paulo |
| Pierre | Martinetti | Università di Genova & INFN |
| Paolo | Meda | University of Pavia |
| Catherine | Meusburger | Friedrich-Alexander-Universität |
| Albert | Much | Institute for Theoretical Physics – Leipzig |
| Filippo | Nava | University of York |
| Karl-Hermann | Neeb | Friedrich-Alexander-Universität |
| Jonas | Neuser | Friedrich-Alexander-Universität |
| Lorenzo | Pettinari | University of Trento |
| Andrea | Pizzamiglio | Università di Pavia |
| Michael | Preeg | Friedrich-Alexander-Universität |
| Karl-Henning | Rehren | ITP Universität Göttingen |
| Christoph | Richter | Universität Leipzig |
| Melissa | Rodriguez Zarate | Friedrich-Alexander-Universität |
| Leonardo | Sangaletti | Leipzig University |
| Lucas | Seco | University of Brasilia |
| Alexander | Seifert | Friedrich-Alexander-Universität |
| Tobias | Simon | Friedrich-Alexander-Universität |
| Binh | Tran | Leibniz Universität Hannover |
| Lorenzo Siro | Trezzini | Università di Pavia |
| Rainer | Verch | Universität Leipzig |
| Wolfgang | Wieland | Friedrich-Alexander-Universität |
| Fabrizio | Zanello | University of Potsdam |
| Cong | Zhang | Friedrich-Alexander-Universität |
Abstracts
Osterwalder-Schrader axioms for unitary full VOAs
Maria Stella Adamo
Osterwalder-Schrader (OS) reconstruction results provide conditions to be verified by Euclidean n-point correlation functions to produce a quantum field theory in the Wightman formalism. On the other hand, full Vertex Operator Algebras (VOAs) can be seen as extensions of a chiral and anti-chiral VOA, giving a rigorous description of compact 2D quantum field theories.
In this talk, we define unitarity for full VOAs and show that for a reasonable class of unitary full VOAs, we can define n-point correlation functions that verify a conformal version of the OS axioms and the linear growth condition.
Vertex algebras and non-unitary Wightman CFTs
Sebastiano Carpi
I will discuss a definition of Moebius covariant Wightman field theories on the circle which naturally generalizes the ordinary one to possibly non-unitary theories. I will then describe a recent result on the equivalence of the category of (non-negatively graded, bosonic) Moebius vertex algebras equipped with a generating family of quasi-primary vectors and the category of these generalized Wightman CFTs. In restriction to the unitary setting this equivalence improves recent results by Raymond, Tanimoto and Tener. Moreover the result applies to many examples of non-unitary and not necessarily simple vertex algebras. The talk is based on recent work with Raymond, Tanimoto and Tener.
Trace anomaly for the Stress-Energy Tensor of a Self-interacting Scalar field on a curved spacetime
Beatrice Costeri
Abstract: In several models of interest in theoretical physics, the trace or conformal anomaly of an interacting QFT plays a prominent role in the functional form of specific observables which can be tested in experiments. Yet, current techniques in theoretical physics do not allow for a precise and algorithmic computation of these observables. We prove that perturbative AQFT is a computationally efficient framework to evaluate these quantities. As a concrete example, we compute the trace anomaly of the stress-energy tensor for a self-interacting scalar field theory on a globally hyperbolic spacetime (M,g) up to the second order in the interaction parameter. Based on a joint work with C. Dappiaggi and M. Goi, currently in preparation.
How do the physicists compute the famous Lamb shift?
Jan Derezinski
Precise computations of radiative corrections to the levels of energies of bound states is one of the greatest achievements of the human science (maybe, the greatest). They agree with the experiment up to about 12 digits.
I will try to formulate the theory of bound states as a rigorous problem in (perturbative) QED. These proposals are based on my conversations with specialists, especially prof. Pachucki and prof. Shabaev. I will also tell some entertaining anecdotes related to this question.
Markus B. Fröb
Abstract: The modular Hamiltonian ia a central object in Tomita-Takesaki modular theory, which has found various applications in quantum field theory such as the computation of relative entropy. Modular Hamiltonians are associated to a spacetime region and a quantum state. The known examples comprise essentially the modular Hamiltonian associated to wedge regions and the Minkowski vacuum state for arbitrary Wightman theories (the Bisognano-Wichmann theorem), and the one associated to massless conformal theories and the conformal vacuum in diamonds and light cones. In particular, even for a free massive theory the modular Hamiltonian associated to diamonds is unknown (but numerical results are available).
I present recent analytical results for fermions of small mass restricted to diamonds in 1+1-dimensional Minkowski spacetime in the Minkowski vacuum state, and for a two-parameter family of zero-energy states (generically mixed) for massless fermions on a cylinder. The first result suggests that the full massive modular Hamiltonian might be much more complicated than might be expected; in particular, it might be a highly complicated non-local operator. The second result shows that generically the modular Hamiltonian is non-local, but that in the parametric limit where the state becomes pure, it becomes local. However, even in the local case the two chiralities of the fermion are mixed by the modular flow, which is a behavior that has not been observed previously.
Joint work with D. Cadamuro, Ch. Minz and G. Pérez-Nadal, based on arXiv:2312.04629 and arXiv:2406.19360.
Casimir effect for dielectric media
Arne Hofmann
Abstract: In recent years, our understanding of the Casimir effect has been improved by the use of rigorous methods which moreover yield formulas that are amenable to numerical computations for arbitrary geometries. In this talk I will report on progress made concerning the application of these methods to transmission boundary conditions, which are relevant to the Casimir effect for dielectric media. I will focus on the role of relative trace formulas, which may be of wider interest in spectral geometry.
Driven conformal field theory and circuit complexity
Jani Kastikainen
Abstract: Driven quantum systems exhibit a large variety of interesting and sometimes exotic phenomena. In this talk, I study driven two-dimensional conformal field theories from spacetime and quantum information geometric points of view. I show that a large class of quantum circuits can be realized by coupling the CFT to time-dependent background fields. In particular, unitary time-evolution of the CFT in a background metric is equivalent to a quantum circuit generated by the Virasoro algebra, known as a Virasoro circuit. Similarly, turning on a source for a primary operator deforms the Virasoro circuit in a non-trivial way. I will show how to calculate the Fubini-Study circuit complexity of such a primary-deformed Virasoro circuit and analyze its properties. Some of our results have natural interpretations on quantum information geometries generated by infinite-dimensional Lie algebras. The talk is based on arXiv:2306.00099, arXiv:2409.08319 and on-going work.
Thermal Field theories and Wedge-Modular Inclusions
Ian Koot
Abstract: For many quantum field theories in a vacuum state, it is known that the modular flow associated to the Rindler wedge is realized geometrically by the Lorentz boosts. What is generally unknown, however, is the modular data of the wedge with respect to a thermal/KMS state. In order to research this concept, we introduce a generalization of Halfsided Modular Inclusions, which we call Wedge Modular Inclusions. These inclusions of standard subspaces have an additional symmetry which models spatial translations in the case of the Rindler wedge. In studying these inclusions, we develop some techniques and construct some interesting new examples of standard subspace inclusions.
On the running and the UV limit of Wilsonian renormalization group flows
Andras Laszlo
Abstract: In this talk we describe a recent result [Class.Quant.Grav.41(2024)125009] which states that, under mild conditions, a Wilsonian renormalization group (RG) flow of Feynman correlators, which extends to arbitrary regularization strengths, has a factorization property. Namely, there exists a regularization-independent distributional Feynman correlator (UV limit), from which the flow originates via an algebric ansatz. In addition, we will mention a newer result, stating the analogy of the above theorem in the context of Euclidean Feynman measures. Namely, under mild conditions, a Wilsonian RG flow of Feynman measures extending to arbitrary regularization strenghts has a factorization property: there exists some ultimate Feynman measure (UV limit) on the distributional fields, such that the regularized instances in the flow are obtained from this UV limit via pushforward.
Implementing a Causal Measurement Scheme for Quantum Fields
Jan Mandrysch
Abstract: While measurement processes in standard quantum mechanics are well understood, the extension of these ideas to quantum field theory
(QFT) remains a key challenge. In particular, ensuring that measurements respect fundamental principles such as relativistic causality is crucial. A persistent issue concerning measurements in QFT is, though, that microcausality alone is insufficient to prevent superluminal signaling. In this talk, I will present a concrete scheme for measuring real linear scalar fields, grounded in the Fewster-Verch measurement framework. This approach fully respects the principles of relativistic covariance, locality, and causality, offering a robust solution to the challenges of measurement in QFT.
Deformation Quantization of QFTs in curved spacetimes
Albert Much
Abstract:We provide a deformation quantization, in the sense of Rieffel, for globally hyperbolic spacetimes with a Poisson structure. The Poisson structures have to satisfy Fedosov type requirements in order for the deformed product to be associative. We apply the novel deformation to quantum field theories and their respective states and we prove that the deformed state has a Hadamard singularity structure, if the undeformed state is Hadamard.
Interplay between boundary conditions and the Lorentzian Wetterich equation
Filippo Nava
Abstract: In the framework of the functional renormalization group and of the perturbative, algebraic approach to quantum field theory, in [DDPR23] it has been derived a Lorentian version of a flow equation à la Wetterich, which can be used to study non linear, quantum scalar field theories on a globally hyperbolic spacetime. In this work we show that the realm of validity of this result can be extended to study interacting scalar field theories on globally hyperbolic manifolds with a timelike boundary. By considering the specific examples of half Minkowski spacetime and of the Poincaré patch of Anti-de Sitter, we show that the form of the Lorentzian Wetterich equation is strongly dependent on the boundary conditions assigned to the underlying field theory. In addition, using a numerical approach, we are able to provide strong evidences that there is a qualitative and not only a quantitative difference in the associated flow and we highlight this feature by considering Dirichlet and Neumann boundary conditions on half Minkowski spacetime.
On Classical Aspects of Bose-Einstein Condensation
Lorenzo Pettinari
Abstract: Berezin and Weyl quantizations are renown procedures for mapping classical, commutative Poisson algebras of observable to their non-commutative, quantum counterparts. The latter map is famous for its use on Weyl algebras, while the former is more appopriate for continuous functions decaying at infinity. In this work, we define a variant of Berezin quantization map, which operates on classical Weyl algebras W(E,0) and constitutes a positive strict deformation quantization. We use this map to compare classical and quantum thermal equilibirum states for a bosons gas and its rigouros classical limit.
For this scope, we first define a purely algebraic notion of KMS states for the classical Weyl algebra and verify that in the finite volume setting there is only one possible KMS state, which can be interpreted as the Fourier transform of a Gibbs measure on some Hilbert space. Then, we show how the classical KMS states have thermodynamic limits which can manifest condensation in the zero mode, similarly to what happens in the standard Bose-Einstein condensation. Lastly, we prove that there exist sequences of quantum KMS states, for the infinite volume bose gas, that converge weakly* to classical KMS states. Moreover, the different thermal phases are preserved by this limit, showing that a quantum condensate is mapped to a classical one.
Scaling Limit of de Sitter Quantum Field Theories.
Christoph Richter
Abstract: Our setting is the 1+1-dimensional de Sitter spacetime with increasing radius. From a purely geometric point of view, the corresponding isometry groups of these spacetimes should ultimately converge to the Poincaré group as the radius tends towards infinity, since the curvature approaches zero in this limit. We show that we obtain a group contraction in the sense of Mickelsson and Niederle in this way (see [J. Mickelsson and J. Niederle. “Contractions of representations of de Sitter groups”.
In: Communications in Mathematical Physics 27.3 (Sept. 1972), pp. 167–180.] for reference). In the second part of the talk we construct Algebraic Quantum Field Theories in a preferred, de Sitter-invariant vacuum representation on these spacetimes. The existence of such a vacuum state was shown in [Hans-Juergen Borchers and Detlev Buchholz. Global Properties of Vacuum States
in de Sitter Space. 1999. arXiv: gr-qc/9803036 [gr-qc]]. We expect that the geometric behaviour of our setting should also be encoded in these theories. Namely, we construct such a theory for each radius and perform a scaling limit (for the scaling algebra method see [Detlev Buchholz and Rainer Verch. “Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory”. In: Reviews in Mathematical Physics 07.08 (Nov. 1995), pp. 1195–1239]). We show that in the GNS-representation of a vacuum scaling limit state, the corresponding algebraic quantum field theories on the curved spacetimes reduce to an algebraic quantum field theory on $1+1$-dimensional Minkowski spacetime in vacuum representation.
An L4 quantum energy inequality for the thermal sector
Leonardo Sangaletti
Abstract: Energy density and its positivity properties represent a fundamental subject in classical and quantum physics. In this talk, we will investigate this topic in the thermal representation of a free massive quantum scalar field. After a brief review of the fundamental mathematical tools at the base of this work, we will construct the GNS representation of our QFT induced by a state at thermal equilibrium (KMS). Therein, we will identify the generator of the time evolution and its spatial density. The symmetry between the “particles” and “holes” makes evident the impossibility for a lower bound for the expectation value of the energy density in this representation. In order to tackle this problem, we will investigate and extend some results of modular theory and non-commutative Lp spaces. In this way, we will obtain a general result concerning the expectation value of operators affiliated to a von Neumann algebra. Finally, the proven results will be applied to our setting to derive an L4 state dependent non-trivial QEI.
Quantum Cellular Automata and their Classification
Lorenzo Trezzini and Andrea Pizzamiglio
Abstract: The most general discrete-time, finite-range, unitary dynamics of a lattice of countably many d-level quantum systems is referred to as a Quantum Cellular Automaton (QCA). QCAs have notable applications in Quantum Computation and Quantum Information, particularly in simulating quantum many-body systems in both particle and condensed matter physics. The first rigorous definition of QCAs was established within the framework of Operator Algebra by Schumacher and Werner (arXiv:quant-ph/0405174, 2004).
Up to date, a complete characterization remains elusive, despite considerable efforts over recent years to understand their group structure.
In this talk, we provide an overview of the theory of QCAs and present our results on their classification in physically relevant unexplored contexts. Specifically, exploiting Operator Algebra methods, we classify all admissible unitary local maps for QCAs on hypercubic lattices of qubits (arXiv:2408.04493) ,and also enhance previous results regarding Fermionic QCAs (in preparation work). This talk is based on joint works with Paolo Perinotti, Alessandro Bisio, Alessandro Tosini and Paolo Meda.
Quantum non-causality in spacetime may be not exclusively quantum
Rainer Verch
There are several non-causal effects that have been attributed to quantum physics. These include the analogues of “closed timelike curve effects” in quantum circuits proposed by David Deutsch (D-CTC), and the “impossible measurements” in relativistic quantum field theory discussed by Raphael Sorkin. Based on previous work, it will be pointed out in the talk that the alleged non-causality features arise not only in quantum systems, but in the very same manner in systems that are described in the framework of classical (non-quantum) statistical mechanics or classical field theory. Therefore, although the said non-causality scenarios have been portrayed as pertaining to quantum systems or quantum fields, they are in fact not based on, nor characteristic of, the quantum nature of physical systems.
Registration: Registration is still open by the form below, but we can no longer accept further talks.