Limiting absorption principle and equivalence of Feynman propagators on asymptotically Minkowski spacetimes

TL;DR

This paper proves the limiting absorption principle for wave operators on asymptotically Minkowski spacetimes using Mourre theory, and shows the equivalence of the anti-Feynman propagator with the outgoing resolvent, improving previous results.

Contribution

It introduces a more transparent method to establish the limiting absorption principle and removes extra conditions from prior work, also proving the equivalence of two propagator definitions.

Findings

Established the limiting absorption principle using Mourre theory.

Removed additional conditions required in previous studies.

Proved the anti-Feynman propagator coincides with the outgoing resolvent.

Abstract

In this paper, we shall show that the limiting absorption principle for the wave operator on the asymptotically Minkowski spacetime. This problem was previously considered by [A. Vasy, J. Spect. Theory, 10,439-461 , (2020)]. Here, we employ a more transparent tool, the Mourre theory and removes an additional condition which is imposed in his paper. Moreover, we also prove that the anti-Feynman propagator defined by G\'erard and Wrochna coincides with the outgoing resolvent.