A new algebraic approach for calculating the heat kernel in quantum gravity

TL;DR

This paper introduces an algebraic method to compute the heat kernel in quantum gravity by representing it as an average over isometry groups in symmetric spaces, simplifying calculations of the effective action.

Contribution

It presents a novel algebraic approach that expresses the heat kernel as an average over isometry groups, applicable to covariantly constant curved backgrounds in quantum gravity.

Findings

Derived explicit form of the heat kernel diagonal in symmetric spaces.

Connected the heat kernel representation to the structure of symmetric spaces.

Discussed implications for calculating the effective action in quantum gravity.

Abstract

It is shown that the heat kernel operator for the Laplace operator on any covariantly constant curved background, i.e. in symmetric spaces, may be presented in form of an averaging over the Lie group of isometries with some nontrivial measure. Using this representation the heat kernel diagonal, i.e. the heat kernel in coinciding points is obtained. Related topics concerning the structure of symmetric spaces and the calculation of the effective action are discussed.