The heat kernel on symmetric spaces via integrating over the group of isometries

TL;DR

This paper introduces an algebraic method to compute the heat kernel on Riemannian manifolds with covariantly constant curvature by integrating over the isometry group, simplifying calculations of this fundamental operator.

Contribution

It presents a novel algebraic approach that expresses the heat kernel as an average over the isometry group, applicable to manifolds with covariantly constant curvature.

Findings

Heat kernel can be derived via averaging over isometry groups.

The method simplifies calculations on symmetric spaces.

Explicit integral representation of the heat kernel diagonal.

Abstract

A new algebraic approach for calculating the heat kernel for the Laplace operator on any Riemannian manifold with covariantly constant curvature is proposed. It is shown that the heat kernel operator can be obtained by an averaging over the Lie group of isometries. The heat kernel diagonal is obtained in form of an integral over the isotropy subgroup.