Equivariant heat invariants of the Laplacian and nonmininmal operators on differential forms

TL;DR

This paper computes equivariant heat kernel coefficients for the Laplacian and nonminimal operators on differential forms, extending known formulas to include torsion and providing explicit coefficients and formulas.

Contribution

It introduces new calculations of equivariant heat kernel coefficients for the Bochner Laplacian with torsion and nonminimal operators, including the Gilkey-Branson-Fulling formula.

Findings

Computed first two equivariant heat kernel coefficients for the Bochner Laplacian.

Extended calculations to include torsion in the Laplacian.

Derived the equivariant Gilkey-Branson-Fulling formula for nonminimal operators.

Abstract

In this paper, we compute the first two equivariant heat kernel coefficients of the Bochner Laplacian on differential forms. The first two equivariant heat kernel coefficients of the Bochner Laplacian with torsion are also given. We also study the equivariant heat kernel coefficients of nonmininmal operators on differential forms and get the equivariant Gilkey-Branson-Fulling formula.