Diagrams for heat kernel expansions

TL;DR

This paper introduces a diagrammatic technique for heat kernel expansion, facilitating small-derivative expansions and reproducing covariant perturbation results, with applications in stress-energy tensor evaluations.

Contribution

A novel diagrammatic method for heat kernel expansion that simplifies calculations and reproduces existing covariant perturbation theory results.

Findings

Provides a new diagrammatic expansion for the heat kernel at coincident points

Enables calculation of heat kernel derivatives for stress-energy tensor evaluation

Reproduces results of covariant perturbation theory

Abstract

A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as covariant perturbation theory. The new technique gives an expansion for the heat kernel at coincident points. It can also be used to obtain the derivative of the heat kernel and this is useful for evaluating the expectation values of the stress-energy tensor.