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

Coherent states in fermionic Fock-Krein spaces and their amplitudes

We generalize the fermionic coherent states to the case of Fock-Krein spaces, i.e., Fock spaces with an idefinite inner product of Krein type. This allows for their application in topological or functorial quantum field theory and more specifically in general boundary quantum field theory. In this context we derive a universal formula for the amplitude of a coherent state in linear field theory on an arbitrary manifold with boundary.Comment: 20 pages, LaTeX + AMS + svmult (included), contribution to the proceedings of the conference "Coherent States and their Applications: A Contemporary Panorama" (Marseille, 2016); v2: minor corrections and added axioms from arXiv:1208.503

Two-dimensional quantum Yang-Mills theory with corners

The solution of quantum Yang-Mills theory on arbitrary compact two-manifolds is well known. We bring this solution into a TQFT-like form and extend it to include corners. Our formulation is based on an axiomatic system that we hope is flexible enough to capture actual quantum field theories also in higher dimensions. We motivate this axiomatic system from a formal Schroedinger-Feynman quantization procedure. We also discuss the physical meaning of unitarity, the concept of vacuum, (partial) Wilson loops and non-orientable surfaces.Comment: 31 pages, 6 figures, LaTeX + AMS; minor corrections, reference update

The Unruh-deWitt Detector and the Vacuum in the General Boundary formalism

We discuss how to formulate a condition for choosing the vacuum state of a quantum scalar field on a timelike hyperplane in the general boundary formulation (GBF) using the coupling to an Unruh-DeWitt detector. We explicitly study the response of an Unruh-DeWitt detector for evanescent modes which occur naturally in quantum field theory in the presence of the equivalent of a dielectric boundary. We find that the physically correct vacuum state has to depend on the physical situation outside of the boundaries of the spacetime region considered. Thus it cannot be determined by general principles pertaining only to a subset of spacetime.Comment: Version as published in CQ

Probabilities in the general boundary formulation

We give an introductory account of the general boundary formulation of quantum theory. We refine its probability interpretation and emphasize a conceptual and historical perspective. We give motivations from quantum gravity and illustrate them with a scenario for describing gravitons in quantum gravity.Comment: 7 pages, LaTeX + jpconf, contribution to proceedings of DICE2006, Piombino, Italy, September 2006; v2: typos corrected (including title) and references update

General boundary quantum field theory: Timelike hypersurfaces in Klein-Gordon theory

We show that the real massive Klein-Gordon theory admits a description in terms of states on various timelike hypersurfaces and amplitudes associated to regions bounded by them. This realizes crucial elements of the general boundary framework for quantum field theory. The hypersurfaces considered are hyperplanes on the one hand and timelike hypercylinders on the other hand. The latter lead to the first explicit examples of amplitudes associated with finite regions of space, and admit no standard description in terms of ``initial'' and ``final'' states. We demonstrate a generalized probability interpretation in this example, going beyond the applicability of standard quantum mechanics.Comment: 25 pages, LaTeX; typos correcte

Spatially asymptotic S-matrix from general boundary formulation

We construct a new type of S-matrix in quantum field theory using the general boundary formulation. In contrast to the usual S-matrix the space of free asymptotic states is located at spatial rather than at temporal infinity. Hence, the new S-matrix applies to situations where interactions may remain important at all times, but become negligible with distance. We show that the new S-matrix is equivalent to the usual one in situations where both apply. This equivalence is mediated by an isomorphism between the respective asymptotic state spaces that we construct. We introduce coherent states that allow us to obtain explicit expressions for the new S-matrix. In our formalism crossing symmetry becomes a manifest rather than a derived feature of the S-matrix.Comment: 27 pages, LaTeX + revtex4; v2: various corrections, references update

Discrete Dynamics: Gauge Invariance and Quantization

Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and internal symmetries. We describe the main features of the gauge principle relevant to the discrete and finite background. Assuming that continuous phenomena are approximations of more fundamental discrete processes, we discuss -- with the help of a simple illustration -- relations between such processes and their continuous approximations. We propose an approach to introduce quantum structures in discrete systems, based on finite gauge groups. In this approach quantization can be interpreted as introduction of gauge connection of a special kind. We illustrate our approach to quantization by a simple model and suggest generalization of this model. One of the main tools for our study is a program written in C.Comment: 15 pages; CASC 2009, Kobe, Japan, September 13-17, 200

Spin Foam Diagrammatics and Topological Invariance

We provide a simple proof of the topological invariance of the Turaev-Viro model (corresponding to simplicial 3d pure Euclidean gravity with cosmological constant) by means of a novel diagrammatic formulation of the state sum models for quantum BF-theories. Moreover, we prove the invariance under more general conditions allowing the state sum to be defined on arbitrary cellular decompositions of the underlying manifold. Invariance is governed by a set of identities corresponding to local gluing and rearrangement of cells in the complex. Due to the fully algebraic nature of these identities our results extend to a vast class of quantum groups. The techniques introduced here could be relevant for investigating the scaling properties of non-topological state sums, being proposed as models of quantum gravity in 4d, under refinement of the cellular decomposition.Comment: 20 pages, latex with AMS macros and eps figure

Deformed Schrodinger symmetry on noncommutative space

We construct the deformed generators of Schroedinger symmetry consistent with noncommutative space. The examples of the free particle and the harmonic oscillator, both of which admit Schroedinger symmetry, are discussed in detail. We construct a generalised Galilean algebra where the second central extension exists in all dimensions. This algebra also follows from the Inonu--Wigner contraction of a generalised Poincare algebra in noncommuting space.Comment: 9 pages, LaTeX, abstract modified, new section include