The Feynman propagator on perturbations of Minkowski space

TL;DR

This paper establishes the existence of the Feynman propagator on Lorentzian scattering spaces and demonstrates well-posedness of related nonlinear wave equations in quantum field theory for small data.

Contribution

It proves the existence of the Feynman propagator as a bounded operator on specific function spaces and shows well-posedness of nonlinear QFT wave equations in this framework.

Findings

Feynman propagator exists as a bounded map between specialized Banach spaces.

Nonlinear wave equations in QFT are well-posed for small initial data.

The analysis applies to Lorentzian scattering spaces with decay and microlocal regularity.

Abstract

In this paper we analyze the Feynman wave equation on Lorentzian scattering spaces. We prove that the Feynman propagator exists as a map between certain Banach spaces defined by decay and microlocal Sobolev regularity properties. We go on to show that certain nonlinear wave equations arising in QFT are well-posed for small data in the Feynman setting.