The Feynman propagator on perturbations of Minkowski space

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.

Final published version. 50 pages, 4 figures. Typos corrected and explanatory remarks added

References in corpus (4)

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• Cosmological horizons and reconstruction of quantum field theories
• Gupta-Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times
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Cited by in corpus (10)

• Analysis of linear waves near the Cauchy horizon of cosmological black holes
• Hadamard states for the Klein-Gordon equation on Lorentzian manifolds of bounded geometry
• Feynman Propagators on Static Spacetimes
• The holographic Hadamard condition on asymptotically Anti-de Sitter spacetimes
• Limiting absorption principle and equivalence of Feynman propagators on asymptotically Minkowski spacetimes
• A remark on the essential self-adjointness for Klein-Gordon type operators
• Dynamical residues of Lorentzian spectral zeta functions
• Wick rotation of the time variables for two-point functions on analytic backgrounds
• An index theorem on asymptotically static spacetimes with compact Cauchy surface
• Microlocal analysis near null infinity in asymptotically flat spacetimes