Generalized heat kernel coefficients

TL;DR

This paper extends the heat kernel expansion for bosonic operators by allowing the mass to be a matrix in flavor space, providing a generalized framework that maintains gauge invariance and relates to standard coefficients.

Contribution

It introduces a generalized heat kernel expansion with matrix-valued masses, broadening the applicability of the standard expansion in quantum field theory.

Findings

Generalized coefficients relate simply to standard ones.

Gauge invariance remains manifest in the generalized expansion.

Applicable to all orders and flavor spaces.

Abstract

Following Osipov and Hiller, a generalized heat kernel expansion is considered for the effective action of bosonic operators. In this generalization, the standard heat kernel expansion, which counts inverse powers of a c-number mass parameter, is extended by allowing the mass to be a matrix in flavor space. We show that the generalized heat kernel coefficients can be related to the standard ones in a simple way. This holds with or without trace and integration over spacetime, to all orders and for general flavor spaces. Gauge invariance is manifest.