A note on the heat kernel coefficients for nonminimal operators

TL;DR

This paper evaluates and verifies heat kernel coefficients for nonminimal operators across different methods and dimensions, establishing connections between various computational techniques and confirming consistency with previous results.

Contribution

It provides a detailed comparison and validation of heat kernel coefficients for nonminimal operators using multiple approaches, including symbolic computation and Green function construction.

Findings

Validated 4D heat kernel coefficients against existing results.

Established connection between Shore's Green function approach and other techniques.

Confirmed gauge parameter dependence of coefficients through dimensional analysis.

Abstract

We consider certain results for the heat kernel of nonminimal operators. The general expressions provided by Gusynin and Kornyak resulting from symbolic computation programmes for n dimensions are evaluated for 4 dimensions which are checked against results given by Barvinsky and Vilkovisky. We also check that the results in flat space are consistent with earlier results of Guendelmen et al. We then consider a powerful construction of the Green function of a nonminimal operator by Shore for covariantly constantly gauge fields in flat spacetime, and employ dimensional arguments to produce a check on the gauge parameter dependence of a certain coefficient. The connection of the results for heat kernel coefficients emanating from the construction of Shore, to those from other techniques is hereby established for the first time.