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

TL;DR

This paper develops an evolution equation framework for the Klein-Gordon operator on curved spacetimes, enabling the treatment of low regularity metrics and potentials for quantum field theory applications.

Contribution

It introduces a novel evolution equation approach to handle low regularity in the Klein-Gordon equation on curved spacetimes, facilitating propagator construction.

Findings

Established a method for low regularity metrics

Constructed various propagators for quantum field theory

Extended the theory to include electromagnetic and scalar potentials

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.