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

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 Gérard and Wrochna coincides with the outgoing resolvent.

arXiv commentProof of Lemma 3.5 is corrected

References in corpus (6)

• Feynman Propagators on Static Spacetimes
• The Feynman propagator on perturbations of Minkowski space
• Hadamard property of the in and out states for Klein-Gordon fields on asymptotically static spacetimes
• An Evolution Equation Approach to the Klein-Gordon Operator on Curved Spacetime
• Complex powers of the wave operator and the spectral action on Lorentzian scattering spaces
• Essential self-adjointness of real principal type operators

Cited by in corpus (5)

• Complex powers of the wave operator and the spectral action on Lorentzian scattering spaces
• A remark on the essential self-adjointness for Klein-Gordon type operators
• Dynamical residues of Lorentzian spectral zeta functions
• An index theorem on asymptotically static spacetimes with compact Cauchy surface
• Remarks on the geodesically completeness and the smoothing effect on asymptotically Minkowski spacetimes