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Quantum Fields from Global Propagators on Asymptotically Minkowski and Extended de Sitter Spacetimes

Authors
  • Vasy, András1
  • Wrochna, Michał2
  • 1 Stanford University, Stanford, CA, 94305-2115, USA , Stanford (United States)
  • 2 Université Grenoble Alpes, Institut Fourier, UMR 5582 CNRS, CS 40700, Grenoble Cedex 09, 38058, France , Grenoble Cedex 09 (France)
Type
Published Article
Journal
Annales Henri Poincaré
Publisher
Springer International Publishing
Publication Date
Feb 16, 2018
Volume
19
Issue
5
Pages
1529–1586
Identifiers
DOI: 10.1007/s00023-018-0650-1
Source
Springer Nature
License
Yellow

Abstract

We consider the wave equation on asymptotically Minkowski spacetimes and the Klein–Gordon equation on even asymptotically de Sitter spaces. In both cases, we show that the extreme difference of propagators (i.e., retarded propagator minus advanced, or Feynman minus anti-Feynman), defined as Fredholm inverses, induces a symplectic form on the space of solutions with wave front set confined to the radial sets. Furthermore, we construct isomorphisms between the solution spaces and symplectic spaces of asymptotic data. As an application of this result, we obtain distinguished Hadamard two-point functions from asymptotic data. Ultimately, we prove that non-interacting Quantum Field Theory on asymptotically de Sitter spacetimes extends across the future and past conformal boundary, i.e., to a region represented by two even asymptotically hyperbolic spaces. Specifically, we show this to be true both at the level of symplectic spaces of solutions and at the level of Hadamard two-point functions.

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