An Evolution Equation Approach to the Klein–Gordon Operator on Curved Spacetime

Accepted for publication in Pure and Applied Analysis

Abstract

We develop a theory of the Klein–Gordon equation on curved spacetimes. Our main tool is the method of (non-autonomous) evolution equations on Hilbert spaces. This approach allows us to treat low regularity of the metric, of the electromagnetic potential and of the scalar potential. Our main goal is a construction of various kinds of propagators needed in quantum field theory.