Abstract: We present the non-relativistic limit of the second quantized, relativistic, scalar Bosonic wave equation (namely the KG equation) in a globally hyperbolic (ultra-)static spacetime. This results in a quantized non-relativistic Bose gas. By using the mathematical methods implemented by Bechouche, Mauser and Selberg the non-relativistic limiting process could be described in a mathematically rigorous way. Moreover, the methods of the non-relativistic limit are applied to relativistic ground and thermal states. By doing so, ground and thermal states according to the non-relativistic Bosonic system occur. This new result allows it to handle the expectation values of the stress-energy tensor, appearing as source term in the semi-classical Einstein equation, during the non-relativistic limit.

Abstract: We study gravitational wave propagation in Lovelock theories, which are extensions of Einstein’s theory by higher-curvature corrections, to examine if these theories have good properties such as causality and hyperbolicity. We study the propagation on various background spacetime, and find that initial value problem may cease to be well-posed in some case. We also show that the sound speed of gravitational wave depends on the background and it may cause shock formation in these theories. We discuss implications of these phenomena.

Abstract: We consider the problem of classification of static and asymptotically flat Einstein-Maxwell-dilaton spacetimes with a photon sphere. We are using a naturally modified definition of a photon sphere for electrically charged spacetimes with the additional property that the one-form of the electric field is normal to the photon sphere. For simplicity we are restricting ourselves to the case of zero magnetic charge and assume that the lapse function regularly foliates the spacetime outside the photon sphere. With this information we prove that the photon surface has constant mean curvature and constant scalar curvature. We also derive a few equations which we later use to prove the main classification theorem. Finally we prove that the static asymptotically flat Einstein-Maxwell-dilaton spacetimes with a non-extremal photon sphere are spherically symmetric and fully specified by the mass, electric charge and the scalar charge subject to certain inequalities.

Abstract: We consider the electromagnetic field in the presence of polarizable point dipoles. In the corresponding effective Maxwell equations these dipoles are described by three dimensional delta function potentials. We review the approaches handling these: the self adjoint extension, regularization/renormalisation and the zero range potential methods. Their close interrelations are discussed in detail and compared with the electrostatic approach which drops the contributions from the self fields. For a homogeneous two dimensional lattice of dipoles we write down the complete solutions, which allow, for example, for an easy numerical treatment of the scattering of the electromagnetic field on the lattice or for investigating plasmons.

Abstract: For an observable, we show the existence in low order in the coupling constant of the adiabatic limit of Fredenhagen/Lindner approach to construct an perturbative, interacting KMS state in the Rindler Wedge at the Unruh temperature.

Abstract: Recent constructions of integrable QFT models have made essential use of a property of the ground state called modular nuclearity. In this talk, based on joint work with Lechner, I argue that the definition of modular nuclearity can be extended to generally covariant theories and that it has some nice properties: it is preserved under pull-backs and convex combinations and it behaves well under spacetime deformation. It also explained why modular nuclearity holds for all quasi-free Hadamard states of a free scalar field in any globally hyperbolic spacetime. Previous investigations already established it for the Minkowski vacuum.

Abstract: In this first part of a two parted talk on the quantization of the Proca field on curved spacetimes, we will give a smooth introduction to the dynamics of classical massive vector fields in curved spacetimes. We will describe the dynamics in a coordinate independent fashion, using differential forms, and provide a solution to Proca’s equation including external classical sources: Decomposing Proca’s equation into a system consisting of a wave equation and a constraint, we will solve the initial value problem in terms of fundamental solutions of the Proca operator which we will specify using the fundamental solution of the wave equation operator. The results will be used for the investigation of the quantum problem as will be discussed in part two of the talk which is scheduled for early 2016.

Abstract: This talk is concerned with the stability of anti–de Sitter (AdS) spacetime to spherically symmetric perturbations of a real scalar field in general relativity. For small-amplitude initial data, two types of behavior have been observed numerically, depending on the initial data profile: collapse to a black hole via a turbulent cascade of energy, and noncollapse characterized by recurrences that approach the initial state. In this talk, I will first introduce a two timescale approximation that describes the leading nonlinear interactions for small-amplitude perturbations, and is suitable for studying the weakly turbulent instability of AdS—both noncollapsing and collapsing solutions. Within this framework, I will identify a large class of equilibrium solutions, which are quasiperiodic in time, and I will show that they are stable. I argue that these solutions represent “islands of stability” in AdS and that recurrences observed in generic noncollapsing solutions are orbits about these equilibria. Moreover, the stability analysis gives rise to the measured recurrence times. Alternatively, for initial data far from an equilibrium solution, large amounts of energy are driven to high-frequency modes, and the two timescale approximation breaks down. Depending on the higher order dynamics of the full system, this often signals an imminent collapse to a black hole.

Abstract: The first part of this talk intends to provide a self-contained introduction to conformal tractor calculus. This is a manifestly conformally invariant machinery which is based on the construction of suitable vector bundles and covariant derivatives naturally associated to a conformal manifold. It has been developed and refined in mathematics in the last 20 years and played a crucial role in the construction of conformal invariants, for instance. In the second part of the talk we apply these techniques and outline how the construction of a conformal symmetry superalgebra, as considered by de Medeiros and Hollands, for instance, can be equivalently reformulated in terms of tractor calculus. The main advantage of this approach is that this tractor conformal superalgebra can be given an holographic interpretation. Concretely, we show that it is isomorphic to the symmetry superalgebra of an associated Poincare Einstein manifold which contains the original conformal data at the boundary.

Abstract: We develop a renormalisation scheme for time–ordered products in interacting field theories on curved spacetimes which consists of an analytic regularisation of Feynman amplitudes and a minimal subtraction of the resulting pole parts. This scheme is directly applicable to spacetimes with Lorentzian signature, manifestly generally covariant, invariant under any spacetime isometries present and constructed to all orders in perturbation theory. Moreover, the scheme captures correctly the non–geometric state–dependent contribution of Feynman amplitudes and it is well–suited for practical computations, including momentum space computations in cosmological spacetimes.

Abstract: Ambjorn and Wolfram (Annals of Physics 147 (1983) 33) calculated the vacuum polarization of the massless Klein-Gordon field in 1+1 dimensions in a static external electric field via the summation of modes method. Recently, Schlemmer and Zahn (Annals of Physics 359 (2015) 31) showed that this method yields different results to the ones obtained by the Hadamard point-splitting procedure, when applied to the Dirac field. In that method, one calculates the vacuum polarization via a renormalization presciption for the vacuum two-point function. Here, the treatment by Ambjorn and Wolfram was extended to the massive case and both methods were employed to calculate the vacuum polarization for Dirichlet and Neumann boundary conditions in first order perturbation theory. It was found that the two methods yield qualitative different results. For instance, the vacuum polarization was found to vanish on the spatial boundary for Dirichlet boundary conditions, when the Hadamard point-splitting procedure was applied.

Abstract: Particles states transforming in one of the infinite spin representations of the Poincaré group (as classified by E. Wigner) are consistent with fundamental physical principles, but local fields generating them from the vacuum state cannot exist. While it is known that infinite spin states localized in a spacelike cone are dense in the one-particle space, we show that the subspace of states localized in any double cone is trivial. 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. We also show that if a Doplicher-Haag-Roberts representation (localized in a double cone) of a local net is covariant under a unitary representation of the Poincaré group containing infinite spin, then it has infinite statistics.

Abstract: Preconjugate variables X have commutation relations with the energy-momentum P of the respective system which are of a more general form than just the Hamiltonian one. Interesting examples can be found via geometry: motions on the mass-shell for massive and massless systems, and via group theory: invariance under special conformal trans- formations of mass-shell, resp. light-cone. We work mainly in Minkowski space and treat the spin zero case. The limit process from non-zero to vanishing mass turns out to be non-trivial and leads naturally to wedge variables. Conjugate pairs of operators are then constructed on spaces of functions and on Fock space. On Fock states multiplied by polarization vectors coordinate operators Q con- jugate to the momentum operators P exist. Crucial is the norm problem of the states on which the Q’s act: they determine eventually how many independent conjugate pairs exist. It is intriguing that light wedge variables and hence the wedge-local case seems to be preferred.

Abstract: In the context of constructing interacting quantum field theories 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 the Z(N)-Ising model and the A_N-1 -affine Toda field theories, namely models with a richer particle spectrum and which are believed to have bound states. This construction is done by exhibiting wedge-local fields which arise as a deformation of Lechner’s fields with the so called “bound state operator”. Similar techniques also applies to the sine-Gordon model, where fusion processes become even more complicated. In this talk I will review the passages of this construction and explain the open problems.

Abstract: In this second part of a two parted talk on the quantization of the Proca field on curved spacetimes, we investigate the zero mass limit. For this, we first formulate a generally locally covariant quantum field theory in the framework of Brunetti, Fredenhagen & Verch for the Proca field. To study the mass dependence, we choose the Borchers-Uhlmann-algebra as the algebra of observables and show that it is homeomorphic to a Borchers-Uhlmann-algebra of initial data. This will allow us to define a suitable notion of continuity of observables with respect to the mass und ultimately to investigate the mass-zero-limit. For the source-free case, we will formulate necessary and sufficient conditions for the limit to exist and compare the results with the ones obtained from the investigation of the Maxwell field by Sanders, Dappiaggi & Hack. We will also comment on the general case with sources.