# The massive Feynman propagator on asymptotically Minkowski spacetimes

September 01, 2016

We consider the massive Klein-Gordon equation on asymptotically Minkowski spacetimes, in the sense that the manifold is $R^{1+d}$ and the metric approaches that of Minkowski space at infinity in a short-range way (jointly in time and space variables). In this setup we define Feynman and anti-Feynman scattering data and prove the Fredholm property of the Klein-Gordon operator with the associated Atiyah-Patodi-Singer type boundary conditions at infinite times. We then construct a parametrix (with compact remainder terms) for the Fredholm problem and prove that it is also a Feynman parametrix in the sense of Duistermaat and Hörmander.

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@article{Gerard:2016fsj,
author = "Gérard, Christian and Wrochna, Michał",
title = "{The massive Feynman propagator on asymptotically
Minkowski spacetimes}",
year = "2016",
eprint = "1609.00192",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1609.00192;%%"
}

Keywords:

quantum field theory on curved spacetimes