Covariant derivative expansion of the heat kernel

TL;DR

This paper presents explicit formulas for heat kernel coefficients with various derivatives in flat space-time, applicable to non-Abelian scalar and gauge fields, using labeled operators.

Contribution

It introduces a compact, explicit method for calculating heat kernel coefficients with multiple derivatives in flat space-time with non-Abelian backgrounds.

Findings

Explicit expressions for heat kernel coefficients with up to six derivatives.

Applicable to boundaryless flat space-times and non-Abelian fields.

Uses labeled operators for compactness and clarity.

Abstract

Using the technique of labeled operators, compact explicit expressions are given for all traced heat kernel coefficients containing zero, two, four and six covariant derivatives, and for diagonal coefficients with zero, two and four derivatives. The results apply to boundaryless flat space-times and arbitrary non Abelian scalar and gauge background fields.