Forschungsprofilbereich "Mathematische und computergestützte Wissenschaften − Mathematical and Computational Sciences"

Leipzig, 29-30 May, 2015

• Announcement
• Location & Accomodation
• Registration
• Program
• Participants

Announcement

The workshop will start at about 2 pm on Friday, May 29, and end about 4 pm on Saturday, May 30.

As usual for this workshop series, you are invited to submit talks in the areas of quantum field theory, quantum statistical mechanics, quantum information, non-commutative geometry, quantum gravity and cosmology, and related topics of mathematical physics and mathematics.

By tradition, young researchers are particularly encouraged and invited to report on their M.Sc. or PhD thesis results.

Location & Accomodation

The workshop will take place in the Felix-Klein lecture hall in the Paulinum, Augustusplatz 10, in the city center and close to the station.

For accommodation, there are many nearby options, for example:

http://www.motel-one.com/en/hotels/leipzig/

http://www.accorhotels.com/gb/hotel-1784-novotel-leipzig-city/index.shtml

http://www.bestwestern-leipzig.de

http://www.hotel-am-bayrischen-platz.de

http://www.aohostels.com/de/leipzig/

http://www.schlafgut-leipzig.de/en/index.html

In many hotels in Leipzig you can get a small discount if you book on behalf of Universität Leipzig, using the code BUND2015. However, booking via travel websites such as hrs.de is often cheaper.

Friday evening, there is a conference dinner, taking place at Thüringer Hof.

Registration

To register, please send an email to jochen.zahn@itp.uni-leipzig.de indicating the following:

Name:
Affiliation:

Program

Some of the slides are available here.

Abstracts

• Wojciech Dybalski: "Towards a consistent description of Coulomb scattering in QFT"
  While collisions of one electron and photons (Compton scattering) are well understood in the setting of non-relativistic QED, the case of two electrons (Coulomb scattering) is not under control in any rigorous framework of QFT. This talk will start from a heuristic introduction to this topic, following the Faddeev-Kulish approach, and continue towards recent rigorous results of A. Pizzo and myself on scattering of two electrons in the massless infrared-regular Nelson model.
• Daniela Cadamuro: "Wedge-local fields in the sine-Gordon model"
  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 the sine-Gordon model, which differs from previous models also on the fact that the S-matrix is ``non-diagonal'', yielding some further technical complication.
• Vincenzo Morinelli: "On Localization Of Infinite Spin Particles"
  Given a unitary, positive energy, irreducible representation $U_0$ of the Poincaré group on a Hilbert space $\mathcal H$, one can associate a canonical real, closed, linear subspace $H(O)$ with any open region $O$ of the Minkowski spacetime $\mathbb R^{s+1}$. If $U_0$ is massless with infinite spin, Brunetti Guido and Longo showed that $H(O)$ is cyclic if $O$ is a spacelike cone (an unbounded region). It remained open whether $H(O)$ is non-trivial when $O$ is bounded. We show that indeed $H(O)= \{0\}$ for any bounded region $O$. This implies that the free field theory associated with infinite spin has no observables localized in bounded regions. In an interacting theory, if the vacuum vector is cyclic for a double cone local algebra, then the theory does not contain infinite-spin representations. These results hold under the natural assumption of the Bisognano-Wichmann property, and we present a counter-example (with continuous particle degeneracy) without this property where the conclusions fail. Our results hold true in any spacetime dimension $s+1$ where infinite spin representations exist, namely $s\geq 2$. (Based on a joint work with R.Longo and K.-H. Rehren)
• Christian Köhler: "On the Localization Properties of Quantum Field Theories with Infinite Spin"
  While pointlike localized free fields can be constructed for the positive mass and massless helicity representations of the Poincaré group, just string-localized fields are known to exist for the infinite spin case, the only remaining class of positive-energy representations. [Mund, Schroer, Yngvason 2006] There is even a No-Go Theorem on the existence of Wightman fields with infinite spin. [Yngvason 1970] However, two-particle wavefunctions with compact modular localization [Brunetti, Guido, Longo 2002] can in fact be constructed. In my talk I want to discuss results of my PhD project (Supervisor: Jakob Yngvason) regarding the construction of fields which create these wavefunctions from the vacuum: It turns out that they are incompatible with relative locality to the known string-localized fields due to the conflicting requirements of covariance and momentum-space analyticity. In addition, these incompatibilities are illustrated by a geometric construction which presents the string-localized fields as limits of their massive counterparts.
• Maximilian Kähler: "Asymptotic Equivalence of KMS States in Rindler spacetime"
  The Unruh effect is one of the most startling predictions of quantum field theory. Its interpretation has been controversially discussed, since the first publications of Fulling, Davies and Unruh in the 1970ties. Buchholz and Solveen in 2013 proposed an application of basic thermodynamic definitions to clarify the meaning of temperature and thermal equilibrium in the Unruh effect. As a result the interpretation of the KMS parameter as an expression of local temperature has been questioned. Recently, Verch and Buchholz established that KMS states of a massless scaler field cannot be distinguished in remote regions of the Rindler spacetime, further questioning the thermal interpretation of the KMS parameter. My main result is to extend this asymptotic equivalence of KMS states to the case of a massive scalar field. The key argument involves establishing local quasi-equivalence of the disputed states in regions that infinitely extend towards an accelerated observers direction of motion.
• Mojtaba Taslimitehrani: "Superconformal QFT in curved spacetime"
  We study the 4d, $N=2$ rigid superconformal Yang-Mills theory on a fixed Lorentzian manifold admitting twistor spinors. Whether this classical symmetry can be maintained at the quantum level (i.e. whether one can perturbatively remove the anomaly), is the main concern of this talk. To answer this question, we need to employ an extended version of the BRST formalism, since local gauge and rigid superconformal symmetries are intertwined. The main result is to establish criteria under which the theory can be consistently quantized. More precisely, we prove that the interacting BRST current is conserved and the interacting BRST charge realizes a nilpotent derivation on the enlarged algebra of interacting fields including unphysical and gauge variant fields (ghosts and anti-fields). We then, construct the algebra of physical gauge-invariant renormalized interacting observables as the cohomology of this charge. The result follows from certain Ward identities obtained by prescribing a renormalization scheme, as well as studying certain cohomology classes of the BRST differential. Joint work with Stefan Hollands.
• Atsushi Higuchi: "Eliminating the infrared divergences in the Faddeev-Popov sector of gauge theory and perturbative gravity in spacetimes with closed spatial sections"
  The naïve propagators for the Faddeev-Popov ghosts for gauge theory and perturbative gravity in spacetimes with closed spatial sections (with Killing vectors in the case of perturbative gravity) are infrared (IR) divergent. It will be pointed out that there are conserved fermionic charges in these theories and that these IR divergences can be eliminated by requiring the physical states to be annihilated by these charges. It will also be shown that these conditions together with the BRST invariance lead to a further requirement that the physical states be invariant under the global gauge transformations in the case of gauge theory and under the spacetime symmetry transformations in the case of perturbative gravity.
• Christoph Stephan: "The Spectral Action, Heat Coefficients and Loop Quantum Gravity"
  In this talk I will consider closed Riemannian manifolds equipped with orthogonal connections (with torsion). I will review Einstein-Cartan-Hilbert theory and the Holst action which are starting points for Loop Quantum Gravity. Next, I will consider Dirac operators which are induced by orthogonal connections. Connes’ spectral action principle states that all physically relevant actions should be deducible from the spectrum of a suitable Dirac operator. The construction of the spectral action builds on the knowledge of the Seeley-deWitt coefficients obtained from an asymptotic expansion of the heat trace. I will present a formula for the spectral action in the presence of torsion, discuss its critical points and describe a possible connection to Loop Quantum Gravity. This project is joint work with Frank Pfäffle.
• Florian Hanisch: "Infinite-dimensional supergeometry in fermionic (classical) field theory"
  Classical field theory can be formulated using one of two, essentially dual, strategies: One may construct an infinite-dimensional phase space and derive from it the Poisson algebra of observables, or dually, start with an algebra in the first place. Rigorous approaches to fermionic theories often follow the second approach since it directly allows for the implementation of anticommuting observables. We will explain an approach to fermionic, classical field theory based on supergeometry. As starting point, it takes the (infinite-dim.) space of sections in a super bundle, equipped with an action. PDE-theory on these spaces facilitates the explicit construction of covariant phase space in terms of solutions of the equations of motions. In good cases, this turns out to be an infinite-dim. supermanifold which can be equipped with a symplectic structure. We finally explain how the concept of "algebra of functions" can be adapted to supergeometry and indicate, that the supersmooth functions on phase space provide a reasonable starting point for the construction of the algebra of observables. The talk is based on joint work with Igor Khavkine.
• Igor Khavkine: "Local and gauge invariant observables in gravity"
  It is well known that General Relativity (GR) does not possess any non-trivial local (in a precise standard sense) and diffeomorphism invariant observables. We propose a generalized notion of local observables, which retain the most important properties that follow from the standard definition of locality, yet is flexible enough to admit a large class of diffeomorphism invariant observables in GR. The generalization comes at a small price, that the domain of definition of a generalized local observable may not cover the entire phase space of GR and two such observables may have distinct domains. However, the subset of metrics on which generalized local observables can be defined is in a sense generic (its open interior is non-empty in the Whitney strong topology). Moreover, generalized local gauge invariant observables are sufficient to separate diffeomorphism orbits on this admissible subset of the phase space. Connecting the construction with the notion of differential invariants, gives a general scheme for defining generalized local gauge invariant observables in arbitrary gauge theories, which happens to agree with well-known results for Maxwell and Yang-Mills theories. [arXiv:1503.03754]
• Nicolò Drago: "The generalized Principle of Perturbative Agreement with application to the thermal mass"
  We deal with a generalization of the Principle of Perturbative Agreement (PPA) stated by Hollands and Wald. The PPA requires that, whenever an interacting theory is given by a quadratic perturbation of the free dynamics (so that the whole theory remains "free", i.e. linear equations of motion), the perturbative construction of the algebra of observables and the exact construction should agree, up to a suitable choice of renormalization constants. We develop a proof of the validity of this principle in the case of scalar fields and quadratic interactions without derivatives which differs in strategy from the one given by Hollands & Wald for the case of quadratic interactions encoding a change of metric. Afterwards we generalize the PPA to the situation where a higher order polynomial interaction is present in addition to the exactly tractable quadratic potential. Finally we apply the previous results in order to extend the construction of an interacting KMS state provided by Fredenhagen and Lindner, to the case of the massless Klein Gordon field.
• Samuel Rutili: "On the thermal two-point function for an interacting and massive scalar field on Schwarzschild spacetime"
  In this talk I will discuss the main problems in building a consistent AQFT in Schwarzschild spacetime for a thermal system ruled by an interacting and massive scalar field, extending the methods and the results of Fredenhagen and Lindner. In particular I will focus on the decay rate of the vacuum two-point function along spatial directions, showing that, despite the non vanishing curvature, a KMS state for the interacting system can be constructed. Eventually I will comment on the applicability of this scheme to generic, stationary, asymptotically Minkowskian spacetimes. Joint work with Claudio Dappiaggi.

Participants

Last updated: June 4