The massive Feynman propagator on asymptotically Minkowski spacetimes

2016/09/01 by Christian Gérard, Gérard, Christian, Michał Wrochna +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1609.00192

openalex publication_date 2016/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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