The Feynman propagator on perturbations of Minkowski space
  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. 
Jesse Gell-Redman, Nick Haber, and Andr\'as Vasy
math.AP