Generalized Heat Kernel Coefficients for a New Asymptotic Expansion

TL;DR

This paper develops a generalized asymptotic expansion method for the one-loop effective action involving elliptic operators with nondegenerate mass matrices, extending the standard Schwinger-DeWitt approach.

Contribution

It introduces a new asymptotic expansion technique for the effective action that accounts for nondegenerate mass matrices, expanding the applicability of existing methods.

Findings

First coefficients of the new series are calculated.

Relationship with Seeley-DeWitt coefficients is clarified.

Method extends standard asymptotic expansion techniques.

Abstract

The method which allows for asymptotic expansion of the one-loop effective action W=ln det A is formulated. The positively defined elliptic operator A= U + M^2 depends on the external classical fields taking values in the Lie algebra of the internal symmetry group G. Unlike the standard method of Schwinger - DeWitt, the more general case with the nondegenerate mass matrix M=diag(m1,m2,...) is considered. The first coefficients of the new asymptotic series are calculated and their relationship with the Seeley-DeWitt coefficients is clarified.