Covariant Algebraic Method for Calculation of the Low-Energy Heat Kernel

TL;DR

This paper introduces a covariant algebraic method to derive a closed-form approximation of the heat kernel for Laplace-like operators, focusing on low-energy regimes and neglecting higher-order derivatives.

Contribution

It presents a novel covariant algebraic approach that yields explicit formulas for the heat kernel and its asymptotic expansion coefficients in low-energy approximation.

Findings

Derived a closed formula for the heat kernel in low-energy approximation.

Obtained explicit asymptotic expansion coefficients involving gauge curvature and potential derivatives.

Provided formulas for the heat kernel diagonal in terms of Yang-Mills curvature and potential.

Abstract

Using our recently proposed covariant algebraic approach the heat kernel for a Laplace-like differential operator in low-energy approximation is studied. Neglecting all the covariant derivatives of the gauge field strength (Yang-Mills curvature) and the covariant derivatives of the potential term of third order and higher a closed formula for the heat kernel as well as its diagonal is obtained. Explicit formulas for the coefficients of the asymptotic expansion of the heat kernel diagonal in terms of the Yang-Mills curvature, the potential term and its first two covariant derivatives are obtained.