Feynman Propagators on Exponentially Decaying Perturbations of Stationary Spacetimes with Compact Cauchy Surface

Abstract

In this paper, we construct Feynman propagators on exponentially decaying perturbations of stationary spacetime with compact Cauchy surface. The propagators are defined as parametrices of the wave operator on exponentially weighted Sobolev spaces defined by complex contours $Γ$. We then apply this theory to the computation of indexes of Dirac operators using a continuous Wick-like rotation to relate it to the Riemannian case.