# Feynman Propagators on Static Spacetimes

August 23, 2016

We consider the Klein-Gordon equation on a static spacetime and minimally
coupled to a static electromagnetic potential. We show that it is essentially
self-adjoint on $C_{\mathrm{c}}^\infty$. We discuss various distinguished
inverses and bisolutions of the Klein-Gordon operator, focusing on the
so-called Feynman propagator. We show that the Feynman propagator can be
considered the boundary value of the resolvent of the Klein-Gordon operator, in
the spirit of the limiting absorption principle known from the theory of
Schrödinger operators. We also show that the Feynman propagator is the limit
of the inverse of the Wick rotated Klein-Gordon operator.

Keywords:

Feynman propagator, Klein-Gordon