Off-diagonal coefficients of the DeWitt-Schwinger and Hadamard representations of the Feynman propagator

TL;DR

This paper enhances the DeWitt-Schwinger and Hadamard representations of the Feynman propagator for a massive scalar field in curved spacetime by deriving higher-order covariant Taylor series terms, aiding applications in gravitational wave theory, stochastic gravity, and quantum field theory.

Contribution

It provides higher-order terms for the covariant Taylor series expansions of DeWitt and Hadamard coefficients, improving the representations of the Feynman propagator in curved spacetime.

Findings

Derived higher-order covariant Taylor series terms for coefficients.

Improved the accuracy of Feynman propagator representations.

Facilitated applications in gravitational wave and quantum gravity theories.

Abstract

Having in mind applications to gravitational wave theory (in connection with the radiation reaction problem), stochastic semiclassical gravity (in connection with the regularization of the noise kernel) and quantum field theory in higher-dimensional curved spacetime (in connection with the Hadamard regularization of the stress-energy tensor), we improve the DeWitt-Schwinger and Hadamard representations of the Feynman propagator of a massive scalar field theory defined on an arbitrary gravitational background by deriving higher-order terms for the covariant Taylor series expansions of the geometrical coefficients -- i.e., the DeWitt and Hadamard coefficients -- that define them.