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

Abstract: Assuming general relativity, the dynamical behavior of a homogeneous and isotropic spacetime is governed by the Friedmann equation. Solutions to this equation depend on the specific form of the energy density of the matter assumed to fill the universe. Different models of matter can lead to very different behavior of solutions. We want to study the solutions of the semiclassical Friedmann equation and compare them to the solutions of the Lambda-CDM model. Unfortunately, only a few special solutions are known for the semiclassical Friedmann equation. A suitable mathematical tool to still compare qualitative features of solutions is the theory of dynamical systems. It is shown, that semiclassical cosmology indeed can reproduce qualitative statements of the Lambda-CDM model. Furthermore, solutions of the semiclassical Friedmann equation can reveal new behavior of solutions that might be capable to explain open questions of cosmology.

Abstract: The Schwarzschild spacetime models the exterior region of a spherically symmetric, static star or black hole in general relativity. It possesses a very special, timelike hypersurface which is ruled by and “traps” null geodesics. This surface is called the “photon sphere”. We will show that the Schwarzschild spacetime of positive mass is the only static vacuum asymptotically flat general relativistic spacetime that possesses a suitably geometrically defined photon sphere. This result holds in all spacetime dimensions. We will present two proofs, both extending classical static black hole uniqueness results. Part of this work is joint with Gregory J. Galloway. As a corollary, we obtain a new result concerning the static n-body problem.

Abstract: This talk concerns a construction of asymptotic photon fields in representations of relativistic QED proposed by Buchholz and Roberts. It will also be shown that single-electron states (if they exist in these representations) are vacua of the asymptotic photon fields. This observation allows for a consistent construction of the outgoing wave-operator of Compton scattering. (Joint work with Sabina Alazzawi).

Abstract: We study the N=6 superconformal Chern-Simons field theory (the ABJM theory) conformally coupled to a background curved spacetime. To support rigid supersymmetry, such Lorentzian backgrounds have to admit twistor spinors. At the classical level, the symmetry of the theory can be described by a conformal symmetry superalgebra. Our main aim is to study the self-consistency of this theory at the quantum level. To this end, we employ a version of the BRST formalism adopted to curved space-time and work out the cohomology class which contains potential anomalies. We give a proof that there exists a renormalization scheme in which the full classical conformal supersymmetry is preserved at the quantum level. Moreover, we give a perturbative construction of the algebra of physical, that is gauge and superconformal invariant, interacting quantum fields. This is essentially based on the derivation of an explicit formula for the commutator of the quantum BRST charge and interacting quantum fields, and the proof that it is nilpotent.

Abstract: We study a scalar field on deformed 4 D space-time. The IR/UV mixing is overcome by identifying four relevant/marginal operators. Ward identities allow to decouple the Schwinger-Dyson equations. The resulting field theory leads to a matrix model. After taking limits, all correlation functions obey solvable singular integral equations. The two point function is solved by a NONLINEAR integral equation. We obtained a 4 D QFT, which satisfies growth property, covariance and symmetry. We discuss the evidence for reflection positivity for the 2-point function, for a certain range of the coupling constant. (Work done together with Raimar Wulkenhaar)

Abstract: The Casimir force is usually computed out equally from pressure or energy density, by virtue of an assumed balance between work done to produce small displacements of boundaries and variation of energy. It has been pointed out recently (Fulling, Mera and Trendafilova – 2013) that for wedge-shaped boundaries this balance is violated and the two expressions of Casimir force disagree. In this talk I will revise the violation, suggesting a possible explanation in terms of bad adiabatic approximation of moving boundaries. The analysis is carried out for general geometries, with an insightful example in two-dimensions.

Abstract: It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well. (joint work with Romeo Brunetti, Klaus Fredenhagen, Nicola Pinamonti, Katarzyna Rejzner / arxiv:1605.02573)

Abstract: Entanglement is one of the characteristic features of quantum physics and entanglement entropy is a way to quantify entanglement between subsystems. In this talk, entanglement entropy is reviewed from quantum information theoretic point of view to motivate our passage from non-relativistic quantum mechanics to relativistic quantum field theory. The algebraic formulation of quantum field theory offers the robust generalization of information theoretic ideas using the harmony of Tomita-Takesaki theory of von Neumann algebra.

Abstract: In this talk I will compare a global and a local notion of temperature for a free scalar quantum field in curved space-times. The global notion is given by the KMS condition on stationary space-times, whereas the local notion follows the proposal of Buchholz and Schlemmer, extending work of Buchholz, Ojima and Roos. It is well-known that the local temperature is ill-defined in many states, because the Wick square can have negative expectation values. I show that this can happen even for ground states in ultra-static spacetimes. The main result, however, is positive: every stationary state has a well defined local temperature at a point x if the following sufficient conditions are satisfied: (i) the space-time is globally hyperbolic, 4-dimensional and ultrastatic (no Unruh effect), (ii) the metric satisfies the weak energy condition, (iii) the Cauchy surface is compact, (iv) the field is massless with scalar curvature coupling in the open interval (0,1/6), and (v) the metric is flat near x. The proof uses the positive mass theorem of Schoen and Yau.