Global wave parametrices on globally hyperbolic spacetimes

Matteo Capoferri*, Claudio Dappiaggi, Nicolò Drago

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

In a recent work the first named author, Levitin and Vassiliev have constructed the wave propagator on a closed Riemannian manifold M as a single oscillatory integral global both in space and in time with a distinguished complex-valued phase function. In this paper, first we give a natural reinterpretation of the underlying algorithmic construction in the language of ultrastatic Lorentzian manifolds. Subsequently we show that the construction carries over to the case of static backgrounds thanks to a suitable reduction to the ultrastatic scenario. Finally we prove that the overall procedure can be generalised to any globally hyperbolic spacetime with compact Cauchy surfaces. As an application, we discuss how, from our procedure, one can recover the local Hadamard expansion which plays a key role in all applications in quantum field theory on curved backgrounds.

Original languageEnglish
Article number124316
JournalJournal of Mathematical Analysis and Applications
Volume490
Issue number2
DOIs
Publication statusPublished - 15 Oct 2020

Keywords

  • Global Fourier integral operators
  • Globally hyperbolic spacetimes
  • Wave propagator

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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