Covariant perturbation expansion of off-diagonal heat kernel

TL;DR

This paper extends the covariant perturbation expansion method to off-diagonal heat kernels in flat space, providing a systematic approach up to any order, which was previously limited to diagonal heat kernels.

Contribution

It introduces a novel expansion for off-diagonal heat kernels using covariant perturbation theory, filling a gap in existing literature.

Findings

Provides a systematic expansion for off-diagonal heat kernels

Extends covariant perturbation methods beyond diagonal cases

Enables new calculations in quantum field theory

Abstract

Covariant perturbation expansion is an important method in quantum field theory. In this paper an expansion up to arbitrary order for off-diagonal heat kernels in flat space based on the covariant perturbation expansion is given. In literature, only diagonal heat kernels are calculated based on the covariant perturbation expansion.