The Unruh Effect in General Boundary Quantum Field Theory

In the framework of the general boundary formulation (GBF) of scalar quantum field theory we obtain a coincidence of expectation values of local observables in the Minkowski vacuum and in a particular state in Rindler space. This coincidence could be seen as a consequence of the identification of the Minkowski vacuum as a thermal state in Rindler space usually associated with the Unruh effect. However, we underline the difficulty in making this identification in the GBF. Beside the Feynman quantization prescription for observables that we use to derive the coincidence of expectation values, we investigate an alternative quantization prescription called Berezin-Toeplitz quantization prescription, and we find that the coincidence of expectation values does not exist for the latter

On Unitary Evolution in Quantum Field Theory in Curved Spacetime

We investigate the question of unitarity of evolution between hypersurfaces in quantum field theory in curved spacetime from the perspective of the general boundary formulation. Unitarity thus means unitarity of the quantum operator that maps the state space associated with one hypersurface to the state space associated with the other hypersurface. Working in Klein-Gordon theory, we find that such an evolution is generically unitary given a one-to-one correspondence between classical solutions in neighborhoods of the respective hypersurfaces. This covers the case of pairs of Cauchy hypersurfaces, but also certain cases where hypersurfaces are timelike. The tools we use are the Schroedinger representation and the Feynman path integral.Comment: 12 pages, LaTeX + revtex4; v2: minor improvements and correction

S-matrix at spatial infinity

We provide a new method to construct the S-matrix in quantum field theory. This method implements crossing symmetry manifestly by erasing the a priori distinction between in- and out-states. It allows the description of processes where the interaction weakens with distance in space, but remains strong in the center at all times. It should also be applicable to certain spacetimes where the conventional method fails due to lack of temporal asymptotic states.Comment: 4 pages, LaTeX + revtex4; v2: normalization factors corrected; v3: two paragraphs added, minor corrections and enhancements, reference list updated; v4: references corrected/update

S-Matrix for AdS from General Boundary QFT

The General Boundary Formulation (GBF) is a new framework for studying quantum theories. After concise overviews of the GBF and Schr\"odinger-Feynman quantization we apply the GBF to resolve a well known problem on Anti-deSitter spacetime where due to the lack of temporally asymptotic free states the usual S-matrix cannot be defined. We construct a different type of S-matrix plus propagators for free and interacting real Klein-Gordon theory.Comment: 4 pages, 5 figures, Proceedings of LOOPS'11 Madrid, to appear in IOP Journal of Physics: Conference Series (JPCS

States and amplitudes for finite regions in a two-dimensional Euclidean quantum field theory

We quantize the Helmholtz equation (plus perturbative interactions) in two dimensions to illustrate a manifestly local description of quantum field theory. Using the general boundary formulation we describe the quantum dynamics both in a traditional time evolution setting as well as in a setting referring to finite disk (or annulus) shaped regions of spacetime. We demonstrate that both descriptions are equivalent when they should be.Comment: 19 pages, LaTeX + revtex4; minor correction

A simple background-independent hamiltonian quantum model

We study formulation and probabilistic interpretation of a simple general-relativistic hamiltonian quantum system. The system has no unitary evolution in background time. The quantum theory yields transition probabilities between measurable quantities (partial observables). These converge to the classical predictions in the $\hbar\to 0$ limit. Our main tool is the kernel of the projector on the solutions of Wheeler-deWitt equation, which we analyze in detail. It is a real quantity, which can be seen as a propagator that propagates "forward" as well as "backward" in a local parameter time. Individual quantum states, on the other hand, may contain only "forward propagating" components. The analysis sheds some light on the interpretation of background independent transition amplitudes in quantum gravity

Background independence in a nutshell

We study how physical information can be extracted from a background independent quantum system. We use an extremely simple `minimalist' system that models a finite region of 3d euclidean quantum spacetime with a single equilateral tetrahedron. We show that the physical information can be expressed as a boundary amplitude. We illustrate how the notions of "evolution" in a boundary proper-time and "vacuum" can be extracted from the background independent dynamics.Comment: 19 pages, 19 figure

In–out propagator in de Sitter space from general boundary quantum field theory

The general boundary formulation of quantum theory is applied to quantize a real massive scalar field in de Sitter space. The space–time region where the dynamics of the field takes place is bounded by one spacelike hypersurface of constant conformal de Sitter time. The computation of the amplitude in the presence of a linear interaction with a source field with compact support in the region considered provides the expression of the Feynman propagator which coincides with the so-called in–out propagator