2019/12/23 by Jan Dereziński, Dereziński, Jan, Daniel Siemssen +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #Mathematical Physics (math-ph) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1912.10692
openalex publication_date 2019/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
In the first part of our paper we analyze bisolutions and inverses of (non-autonomous) evolution equations. We are mostly interested in pseudo-unitary evolutions on Krein spaces, which naturally arise in linear Quantum Field Theory. We prove that with boundary conditions given by a maximal positive and maximal negative space we can associate an inverse, which can be viewed as a generalization of the usual Feynman propagator. In the context of globally hyperbolic manifolds, the Feynman propagator turns out to be a distinguished inverse of the Klein-Gordon operator. Within the formalism of Quantum Field Theory on curved spacetimes, the Feynman propagator yields the expectation values of time-ordered products of fields between the in and out vacuum --the basic ingredient for Feynman diagrams.