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38th LQP Workshop "Foundations and Constructive Aspects of QFT"

Dates: May 27-28, 2016

As usual, the workshop will feature recent results in Algebraic QFT. Other topics in the scope of the workshop are non-relativistic quantum field theory, quantum statistical mechanics, quantum information, non-commutative geometry, quantum gravity and cosmology, and related topics of mathematical physics and mathematics. We especially encourage Master and Ph.D. students and young Postdocs to present their work.

On the first day of the workshop - Friday before noon - there will be a mini course by Hendrik Grundling (University of New South Wales, Australia) with title

QCD on an infinite lattice : Dynamics and ground states.

We welcome any researchers interested to attend the workshop. If you would like to participate, please register by sending an email to one of the organizers listed below. The email should thereby include the following information:

  • Subject: LQP38 Registration

  • Surname
  • Given name
  • Affiliation (full address)
  • Will you attend the conference dinner?
  • Additional comments

For information about accommodation, location, conference dinner and participants please scroll down.

Organization and Contact


Friday 27.05. Saturday 28.05.
QCD Holography I
09:00 - 10:15
09:00 - 9:40
Coffee break Ferreira
09:40 - 10:20
10:45 - 12:00
Coffee break
Lunch Holography II
10:50 - 11:30
14:00 - 14:40
11:30 - 12:10
14:40 - 15:20
15:20 - 16:00
Non-commutative spacetime
Coffee break Jong
14:40 - 15:20
C*-Algebras Géré
15:20 - 16:00
16:30 - 17:10
Informal discussions
17:10 - 17:50
17:50 - 18:30
Conference dinner


  • Hendrik Grundling: QCD on an infinite lattice : Dynamics and ground states. Slides

In a C*-algebra context, we generalize the finite lattice model for Hamiltonian QCD developed by Kijowski & Rudolph, to an infinite lattice. In particular, we construct its dynamical automorphism group and obtain ground states for it.
We start with the field algebra for the finite lattice in a natural representation. We then generalize this representation to the infinite lattice, and construct a Hilbert space which has represented on it all the local algebras (i.e. kinematics algebras associated with finite connected sublattices) equipped with the correct graded commutation relations. Next, on this Hilbert space we consider a suitably large C*-algebra which contains all the local algebras. On this algebra we prove that there is a one parameter automorphism group, which is the pointwise norm limit of the local time evolutions along a sequence of finite sublattices, increasing to the full lattice. This is our global time evolution. (The proof is an application of methods developed by Nachtergaele & Sims). We then take as our field algebra the C*-algebra generated by the orbits of all the local algebras w.r.t. the global time evolution. Thus the time evolution creates the field algebra. The time evolution is strongly continuous on this choice of field algebra, though not on the original larger C*-algebra. We define the gauge transformations, explain how to enforce the Gauss law constraint, and show that the dynamics automorphism group descends to the algebra of physical observables. Finally, we prove that gauge invariant ground states exist.

  • Marcel Bischoff: Generalized Orbifolds in Algebraic Conformal QFT Slides

We will introduce a notion of fixed points by quantum operations for nets of observables, which generalizes fixed points by finite groups of global gauge automorphisms, so-called orbifolds. We will give a classification of such actions on completely rational chiral conformal nets and discuss structural results like the DHR representation theory for such fixed points nets.

  • Dirk Deckert: Ultraviolet properties of the spinless Yukawa model Slides

In a joint work with A. Pizzo we consider the one-particle sector of the spinless Yukawa model, which describes the interaction of a nucleon with a real field of scalar massive bosons (neutral mesons). The nucleon as well as the mesons have relativistic dispersion relations. In this model we study the dependence of the nucleon mass shell on the ultraviolet cut-off Λ. For any finite ultraviolet cut-off the nucleon one-particle states are constructed in a bounded region of the energy-momentum space. We identify the dependence of the ground state energy on Λ and the coupling constant. More importantly, we show that the model considered here becomes essentially trivial in the limit Λ→∞ regardless of any (nucleon) mass and self-energy renormalization. This result again raises the question in which sense such models can be renormalized non-perturbatively.

  • Hugo Ferreira: Quantum states for a scalar field on AdS Slides

In this talk, we describe the construction of a quantum state for a scalar field on anti-de Sitter (AdS) spacetime, subject to appropriate boundary conditions. We show how this can be achieved by considering a quantum state on the conformal boundary of AdS through a holographic relation. We also investigate whether it enjoys a suitable Hadamard-like condition. We finish by commenting on how this construction can be generalised to asymptotically AdS spacetimes. This work has been made in collaboration with Claudio Dappiaggi.

  • Antoine Géré: Perturbatively finite gauge models on the noncommutative three-dimensional space R^3_λ Slides

We show that natural noncommutative gauge theory models on R^3_λ can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of R^3_λ and the components of the gauge invariant 1-form canonical connection. This latter object shows up naturally within the present noncommutative differential calculus. Restricting ourselves to positive actions with covariant coordinates as field variables, a suitable gauge-fixing leads to a family of matrix models with quartic interactions and kinetic operators with compact resolvent. Their perturbative behavior is then studied. We find that the amplitudes of the ribbon diagrams for the models of a subfamily of these matrix models for which the interactions have a symmetric form are finite to all orders in perturbation. This result extends finally to any of the models of the whole family of matrix models obtained from the above gauge-fixing. The origin of this result is then discussed.

  • Luca Giorgetti: Braided categories of endomorphisms in QFT Slides

In the algebraic formulation of (rational) CFT, the collection of ”local observables” completely determines its positive energy ”particle states” via DHR theory. The latter, mathematically speaking, gives a map between local nets of von Neumann algebras and braided tensor categories of endomorphisms. Spins, dimensions, fusion rules of sectors arise as numerical invariants of the DHR category, considered as an abstract braided tensor category. Here we report on our analysis of the ”braided action” of the DHR category on a single local algebra, interpreted as an additional invariant of the DHR construction. Exploiting the characteristic left/right trivialization feature of the DHR braiding (which has no counterpart in purely categorical contexts) we give a way of deriving completeness of the invariant, i.e., reconstruct the local algebras and the dynamics in the vacuum sector. This is joint work with K.-H. Rehren: [arXiv:1512.01995].

  • Robert Helling: Holographic theories: An Invitation Slides

Since its first appearance in a string theory context in 1998, the AdS/CFT correspondence has been advocated to be of use many areas including heavy ion collisions, hydrodynamics, and superconductors. What all have in common is that the holographic prescription is used to write down an effective theory that is conjectured to describe the relevant long wavelength physics. We will describe the underlying claim that this approach provides a novel way to encode a quantum theory besides the free field (and perturbation theory of weakly coupled (quasi)-particles) and using 2d conformal invariance. If this claim can be substantiated this might also be of relevance for constructive endeavors.

  • Jins De Jong: Partition function approaches to the vacuum sector of Φ^4_4 -theory onthe Moyal plane

The Grosse-Wulkenhaar model is the most promising candidate for an exactly solvable non-trivial quantum field theory in four dimensions. The vacuum sector of this model is the quartic generalization of the Kontsevich model. Studying this from the partition function instead of the Schwinger-Dyson equations highlights different aspects of this and closely related models. In particular, it is expected to contain information about the asymptotics of the two-point function and criticality of the GW-model.

  • Bernard Kay: Entanglement Entropy and Algebraic Holography Slides

The Ryu-Takayanagi equality (RT) equates the (cut off) entanglement entropy between two complementary regions, R1 and R2, of an equal-time surface for a d+1 dimensional CFT on the conformal boundary of d+2 dimensional AdS with 1/4G times the area of the d dimensional bulk minimal surface which has the junction of R1 and R2 as its boundary. We point out that RT implies that, in Rehren’s ”algebraic holography”, the entanglement entropy between two complementary bulk Rehren wedges equals one quarter of the (cut off) area of their shared ridge. This is because, when R1 and R2 are balls, the RT minimal surface is the shared ridge of the bulk Rehren wedges which Rehren-biject to the complementary boundary double-cones whose bases are R1 and R2. We argue this observation supports the suggestion in that the AdS/CFT correspondence is not an equivalence but rather a bijection between just the matter (i.e. non-gravity) operators of the bulk and the boundary CFT operators. If time, we will also discuss connections with the author’s ”matter-gravity entanglement hypothesis”.

  • Nikolai Leopold: Derivation of Maxwells equations from non-relativistic QED Slides

We consider the Pauli-Fierz Hamiltonian which describes a quantum system of nonrelativistic identical particles coupled to the quantized electromagnetic field. We study the time evolution in a mean-field limit where the number N of charged particles gets large while the coupling to the radiation field is rescaled by N^(-1/2). At time zero we assume that almost all charged particles are in the same one-body state (a Bose-Einstein condensate) and we assume also that the Bose excitations of the radiation field are not present (vacuum state) or are close to a coherent state. We then show that at later times and in the limit N → ∞ the charged particles remain in a Bose-Einstein condensate, with the time evolution approximately described by the Hartree-Maxwell system of equations, which models the coupling of a nonrelativistic particle to the classical electromagnetic field. Our result is obtained by an extension of Peter Pickls “method of counting” to condensates of charged particles in interaction with their radiation field. This is a joint work with Peter Pickl.

  • Giuseppe Ruzzi: Non-linear facets of the electromagnetic quantum field Slides

We recall basic concepts underlying the universal C*-algebra of the electromagnetic quantum field putting emphasis on the underlying cohomological ideas. Then we point out how non-linear modifications of the e.m. quantum field lead to meaningful representations of the universal C*-algebra violating a strong form of regularity. In particular, we construct representations with quantum currents and representations with topological charges. The talk is based on an joint work with D. Buchholz, F. Ciolli and E. Vasselli [LMP 2016] and on a work in progress with the same authors.

  • Gabriele Tornetta: The Bivariant Cuntz Semigroup and Classification of Stably Finite C*-algebras Slides

In this talk I will present a bivariant extension of the Cuntz semi-group and show how to use it to classify all unital and stably finite C*-algebras in a way that closely resembles the celebrated Kirchberg-Phillips classification of purely infinite C*-algebras by KK-theory.

  • Jochen Zahn: Generalized Wentzell boundary conditions and holography Slides

We study a free scalar field subject to boundary conditions involving second order derivatives, i.e., of generalized Wentzell type. For the classical system, we establish well-posedness of the Cauchy problem and causal propagation. We quantize the system canonically and discuss the relation between the bulk and the boundary field. Based on arXiv:1512.05512.


The workshop will take place at the Institute for Advanced Study of the TU München (Garching campus, metro stop "Garching-Forschungszentrum" U6).
Directions Pfeil

The map shows the position of the venue.


We kindly ask you to take care of your hotel reservation. We reserved rooms in the Hotels Ibis Munich City North Hotel Pfeil (90,50€ per night and person, incl. breakfast) in Munich and Hotel Hoyacker Hof Pfeil (75€ per night and person, incl. breakfast) in Garching, both with convenient public transport connection to Garching-Forschungszentrum. Please use the keyword LQP-Workshop to guarantee the prices indicated above. We suggest that you make a reservation as early as possible, since the reserved rooms are only available until the 18th of April (Ibis Hotel) and 6th of May (Hotel Hoyacker Hof) respectively and last minute lodging costs may be very high in Munich. Of course, you may choose any other accommodation, but if you are applying for financial support please try to stay within the above price range. In case of any problems with the hotel reservations, do not hesitate to contact us.

Conference dinner

The conference dinner will take place at Hackerhaus Pfeil on Friday the 27th of May.

We thank Technische Universität München and Deutsche Forschungsgemeinschaft for financial support.