abstract: We discuss the role of periods (in the sense of Kontsevich Zagier) in anomalous dimensions and beta-functions of QFT. We compare this with thdsage functions of scales and angles which appear in the computation of amplitudes. We discuss scalar field theories and gauge field theories in this context.

abstract: Linear waves generated by small disturbances on a curved spacetime are well-understood near those disturbances. The behavior of these waves on large scales is typically complicated by the presence of caustics. I show that the leading-order singularity structure of Green functions associated with linear wave equations transforms according to a simple rule after each encounter with a caustic of the light cone. This is established by using Penrose limits to reduce the generic problem to an equivalent one on a plane wave spacetime. The plane wave case can then be analyzed directly.

abstract: In the context of formulating quantum field theories over non-commutative spacetimes, such as Moyal Minkowski space or locally non-commutative versions thereof, one is led to consider a class of partial differential equations of the form (D+W)f=0, where D is a normally hyperbolic differential operator or Dirac operator, and W is some non-local perturbation (“non-commutative potential”). Despite the non-locality, we construct advanced and retarded fundamentaldsag solutions for such PDEs, discuss the structure of their solutions, and compute the scattering behaviour. We also comment on the quantization of these systems. Joint work with Markus Borris and Rainer Verch.

abstract: Flux compactifications relate string theories to observable phenomena and feature non-geometric structures that have lead to the development of generalized geometry to handle the underlying stringy symmetries. We analyze these structures in the context of membrane sigma models and identify a dynamical non-commutative non-associative star product. Non-associativity is here a closed string analog of the non-commutativity of open string endpoints in dsagthe presence of background fields. An application of our construction is a quantization of Nambu-Poisson structures that are relevant in the context of effective open membrane actions. The eventual goal of this work is the computation of stringy corrections to gravity and gauge theories without actually having to do any string theory calculations per se.

abstract: The basic elements of the canonical Loop Quantum Gravity will be presented on an example of gravity coupled to massless scalar field. We will introduce the Hilbert spaces of quantum states and discuss choices of the Dirac observables.

abstract: Our starting point is a generalization of the algebraic approach to perturbative interacting quantum field theory, developed by Brunetti and Fredenhagen, Dütsch and Fredenhagen, and Hollands and Wald, in order to consider perturbations about an arbitrary classical background solution of a given field equation. Within this framework the principle of perturbative agreement implies a notion of background independece. We discuss a geometrical interpretation of this theory, where the geometrical context we are referring to is a infinite dimensional manifold stucture of the set of classical solutions. A strong analogy with the Fedosov’s approach to deformation quantization of finite dimensional symplectic manifolds emerges and it is discussed. Joint work with Prof. Hollands.

abstract: The reduced phase space of a system with symmetries is stratified by orbit types. To examine hypothetical quantum effects of the stratification, one has to construct the associated costratification of the system’s Hilbert space, proposed by Huebschmann. The method will be explained for the adjoint quotient of SU(2), which can be interpreted as SU(2)-lattice gauge theory on a single plaquette. Attempts to generalize this to larger lattices and larger gauge groups will be discussed.

abstract: The entropy outside of an event horizon can never decrease if one includes a term proportional to the horizon area. For a long time, this astonishing result had only been shown for quantum fields that are in an approximately steady state. I will describe a new proof of the generalized second law for arbitrary slices of semiclassical, rapidly-changing horizons. I will start with the simplest case, Rindler horizons, and then describe how the proof can be adapted to other cases (black holes, de Sitter, etc.) by restricting the field algebra to the horizon. The generalized second law holds because the horizon is invariant under a larger symmetry group than the rest of the spacetime.

abstract: This is a non-technical introduction to the Quantum Field Theory approach to the physics of graphene. The Dirac action for the quasiparticles will be derived. Then, calculations of the optical properties, of the conductivity, of the Casimir interaction, and of the Faraday effect will be described.