The massive Feynman propagator on asymptotically Minkowski spacetimes

Christian Gérard (1) , Michał Wrochna (2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 IF - Institut Fourier

We consider the massive Klein-Gordon equation on asymptoti-cally 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.

Mots clés: Feynman propagators; Atiyah-Patodi-Singer boundary conditions; pseudodifferential calculus; scattering theory; Quantum Field Theory on curved spacetimes

Domaines: Physique mathématique [math-ph]

Christian Gérard, Michał Wrochna. The massive Feynman propagator on asymptotically Minkowski spacetimes. 2016. ⟨hal-01337433v2⟩