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

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.