An Improved Heat Kernel Expansion from Worldline Path Integrals

TL;DR

This paper develops an improved method for calculating the heat kernel expansion using worldline path integrals, enabling higher order coefficients computation for scalar fields in gauge backgrounds.

Contribution

It introduces a novel approach to derive the inverse mass expansion via worldline path integrals, extending explicit calculations to higher orders.

Findings

Explicit coefficients computed up to order O(T^8)

Clarification of the relation to previous heat kernel methods

Enhanced technique for scalar effective action calculations

Abstract

The one--loop effective action for the case of a massive scalar loop in the background of both a scalar potential and an abelian or non--abelian gauge field is written in a one--dimensional path integral representation. From this the inverse mass expansion is obtained by Wick contractions using a suitable Green function, which allows the computation of higher order coefficients. For the scalar case, explicit results are presented up to order O(T**8) in the proper time expansion. The relation to previous work is clarified.