Heat Kernel Expansion for Operators in Spaces with Metric Incompatible with Connection

TL;DR

This paper introduces a generalized method for calculating heat kernel coefficients for differential operators in spaces where the metric and connection are incompatible, extending pseudodifferential operator techniques.

Contribution

It proposes a novel approach to compute DWSG coefficients in non-metric compatible spaces, including explicit calculations for specific operators.

Findings

Calculated lowest DWSG coefficients for minimal second and fourth order operators.

Derived coefficients for nonminimal operators of a specified form.

Extended pseudodifferential operator techniques to non-metric compatible geometries.

Abstract

A method for calculation of the DWSG coefficients for operators in spaces with metric incompatible with connection is suggested based on a generalization of the pseudodifferential operators technique. By using the proposed method, the lowest DWSG coefficients are calculated for minimal operators of the second and fourth order and for nonminimal operators of the type $H^{\mu\nu} = - g^{\mu\nu} g_{\alpha\beta}\nabla^{\alpha}\nabla^{\beta} + a\nabla^{\mu}\nabla^{\nu} + X^{\mu\nu}$ in spaces with metric incompatible with connection.