Abstract: It is a generic property of QFT that locally, the energy density may be negative. With regards to negative energy density in the free field, there has been much work done and quantum energy inequalities have been established. Recently, interest has moved onto interacting models which display more interesting behavior. Most work on interacting models has reserved itself to only the single particle case. Here, through the use of the inverse scattering method, we compute explicitly the two particle expectation value of the energy density in the sinh-Gordon model, and show that is must permit a negative energy spectrum.

Abstract: The chiral fermion CFT is special in the sense that it is completely determined by the Cauchy kernel on a given manifold. In my talk, I show how to derive the resolvent of (restrictions of) this kernel on the torus and use it to compute information theoretic quantities, such as the modular Hamiltonian and entanglement entropy.

Abstract: This talk will deal about the question, whether and how a time dynamical descrip- tion of N-particle quantum systems can be established. Dirac already noted in 1932, that the usual Quantum Mechanical wave function $\Psi(t, x_1, …, x_N)$ does not make sense for a Lorentz-covariant description anymore. Instead, a separate time coordinate for each particle has to be introduced, resulting in a so-called Multi-Time Wave Function $\phi(t_1,x_1,…,t_N,x_N)$. The solvability of the corresponding equations of motion is strongly connected to a certain consistency condition. Recently (2013-2016), R. Tumulka, S. Petrat, L. Nickel and D.A. Deckert showed that interaction potentials violate this consistency condition – whereas causal QFT models satisfy them. In my master thesis, I could establish a rigorous proof of existence and unique- ness of a solution to the equations of motion for a QFT toy model. Mathematical complications of such a proof are discussed, as well as general complications when trying to write down a wave function in QFT.

Abstract: Axiomatic formulations of quantum electrodynamics (QED) depart from standard QFTs in various regards. One of them is the presence of Krein spaces (i.e., indefinite metric `Hilbert spaces’) in covariant gauges. While the necessity of such spaces is often claimed, it is difficult to find a satisfactory justification in the literature, especially beyond the Gupta-Bleuler gauge or in the presence of interaction. The aim of this thesis is to provide a systematic treatment of these matters in terms of two no-go theorems.\\ Firstly, we will show that a free hermitian covariant vector field A on a state space with a non-negative metric and a (not necessarily unique) vacuum state will give rise to a vanishing two-point function of its exterior derivative $F_{\mu\nu} = \partial_{[\mu}A_{\nu]}$. Secondly, we will infer from this result that $F$ will not be able to generate massless states from the vacuum even if we let off the assumption of $A$ to be free.

Abstract: A complete description of quantum gravity is still far from being established and the direct observation of quantum gravitational effects requires energy scales currently not accessible in experiments. However, for large distances, low energies and weak gravitational field we can treat gravity perturbatively as an effective field theory with unambiguous predictions at these scales. We work in a spacetime with $g_{\mu\nu}=\eta_{\mu\nu} + \kappa h_{\mu\nu}$ and take the linear metric perturbation $h_{\mu\nu}$ as the graviton field on Minkowski background. We construct an action that includes the graviton field and a point-particle whose Newtonian potential we are interested in ultimately. In order to get a physically meaningful result we construct from the graviton field a gauge-invariant observable using field-dependent coordinates. Its expectation value will give the leading quantum-gravitational correction to the classical Newtonian potential.

Abstract: I will review recent progress in our understanding of light-ray operators in abstract CFTs. Light-ray operators first appeared in QCD and were later studied in N=4 Super Yang-Mills theory and holography by Hofman and Maldacena. More recently, they attracted new interest due to an important role played by the averaged null energy condition (ANEC) operator in various contexts. However, it is only during the last few years it became possible to start developing a more general theory of light-ray operators. I will explain a nonperturbative, convergent operator product expansion (OPE) for null-integrated operators on the same null plane in a CFT. I will discuss its application to energy-energy correlators in N=4 Super Yang-Mills theory and to CFTs with gravity duals.

Abstract: The flow equations of the renormalisation group are a universal tool to rigorously analyse perturbative quantum field theories. We give a short overview and then present (partly astonishing) results of an analysis beyond perturbation theory, in the mean field limit.

Abstract: The question that will be discussed in this talk is: given a chiral conformal net A on the circle, how can we characterize conformal subnets B ⊆ A? An answer will be provided when the local algebras of the conformal embedding give rise to discrete subfactors (namely either finite Jones index or possibly infinite index with some additional regularity assumption), using the notion of compact hypergroup. I will show how to canonically construct a compact hypergroup from data of the subfactor. This hypergroup has a natural action on A and recovers B as the fixed points of its action, thus generalizing orbifolds by compact groups. Additionally it contains information on the representation category of the subfactor. I will then discuss applications of this construction, in particular I will show that when the conformal net A is local then orbifolds by compact quantum groups are ruled out. Based on work in progress with Marcel Bischoff (Ohio University) and Luca Giorgetti (Vanderbilt University).

Abstract: The existence of on-zero neutrino masses is one of the clearest deviations of the Standard Model of particle physics from experimental results. As a consequence, it is used as a starting point to explore possible extensions of the Standard Model. In this talk I present a survey of a certain class of extensions – those leading to so called radiative Majorana neutrino masses – and discuss some of the features one is looking for in such models.

Abstract: While it has been often argued that information loss due to (full) black hole evaporation is not paradoxical in a semi-classical framework, many still claim that information loss, or non-unitary evolution of the quantum state of the universe, is in contradiction with guiding principles of and/or assumptions about a sensible theory of quantum gravity. While in the absence of any definitive theory of quantum gravity one cannot say all that much about the eventual fate of black holes, there are still lessons to be learned from the semi-classical gravity framework, or more generally in the context of quantum fields on curved space-time backgrounds. In particular, we study the global dynamics of a class of quantum field theories on non-globally hyperbolic space-times such as the black hole evaporation space-time and find that in general, not only information loss will occur, but also information gain, in the sense that quantum state of a field `pre-evaporation’ will not uniquely determine a quantum state post-evaporation. This suggests that if we accept black hole evaporation as a physical pehnomenon, we may also have to accept that our universe does not evolve deterministically, even when disregarding wave-function collapse and the measurement problem.

Abstract: Generically, strong cosmic censorship (SCC) is the statement that physics within general relativity should be predicted from initial data prescribed on a Cauchy hypersurface. In this talk I will review how fine-tuned versions of SCC have been formulated and evolved along the last decades up to the point where we believe that Christodoulou’s version is true in asymptotically flat spacetimes. However, I will also describe that in the last 2 years it was found that this is no longer necessarily true for some other backgrounds, namely in some de Sitter (with a positive cosmological) spacetimes or even in rotating BTZ black holes in 3-dimensional Anti-de Sitter spacetime. Finally I will discuss some possibilities (non-smooth initial data, quantum effects,…) that might restore SCC in those backgrounds where the standard formulation of the conjecture is violated.

Abstract: We discuss the Casimir effect in a few toy models using point-split regularization. This method is of particular interest in the definition of Hadamard states on curved spacetimes. These possess a two-point function (in convex neighborhoods) that is modified only according to local geometry. Recently, Sanders used the Positive Mass theorem (PMT) to provide a bound on this background influence for thermal states in static spacetimes. In spacetimes with an outer minimizing boundary, the Penrose-Hawking inequality provides an improved mass estimate over the PMT. The influence on the two-point function may then be investigated using the method of images.

Abstract: In order to calculate the quantum energy inequalities of an integrable QFT, an expansion of the local observables (namely the energy density) in generalized annihilators and creators is often needed. In this talk, we start by giving an overview of the inverse scattering approach and the form factor program for the construction of rigorous integrable QFTs. Afterwards, we sketch a roadmap towards the expansion of local observables in general integrable models, such as the O(N)-invariant nonlinear σ-models, via the use of intertwiner operators. We first examine this method in a simpler case with a single particle species and trivial gauge group as opposed to the O(N) model.

Abstract: The effect of vacuum polarization on binding energies in atoms has long been known and its existence has been well proven by precise experiments on the Lamb shift. Since Uehling’s first approach in 1934, it has been treated perturbatively in orders of the background field (Z\alpha)^n and sometimes even to higher orders in \alpha. In my talk I will present a method for the Coulomb Field which allows a non-perturbative treatment for the coupling to the background field. Introduction of the Hadamard parametrix in position space and a translation into a two-point function in momentum space allows for a numerical evaluation of the induced vacuum polarization charge density, which is illustrated on the example of hydrogen-like lead.