The massive Feynman propagator on asymptotically Minkowski spacetimes

Christian Gérard, Michał Wrochna
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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%%% contains utf-8, see: %%% add \usepackage[utf8]{inputenc} to your latex preamble @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;%%" }

quantum field theory on curved spacetimes