The massive Feynman propagator on asymptotically Minkowski spacetimes II

TL;DR

This paper proves the invertibility of the massive Klein-Gordon operator with Feynman boundary conditions on asymptotically Minkowski spacetimes and characterizes its inverse microlocally, extending previous results with explicit methods.

Contribution

It establishes the existence and properties of the Feynman inverse for the Klein-Gordon operator in a new geometric setting, providing explicit microlocal analysis techniques.

Findings

Invertibility of the Klein-Gordon operator with Feynman boundary conditions

Construction of the Feynman inverse satisfying microlocal conditions

Extension of previous results with explicit analytical methods

Abstract

We consider the massive Klein-Gordon equation on short-range asymptotically Minkowski spacetimes. Extending our results in [GW1], we show that the Klein-Gordon operator with Feynman type boundary conditions at infinite times is invertible and that its inverse, called the Feynman inverse, satisfies the microlocal conditions of Feynman parametrices in the sense of Duistermaat and H\"ormander. This supplements the recent work of Vasy with more explicit techniques.