Borel summation of the small time expansion of the heat kernel with a vector potential

TL;DR

This paper investigates the Borel summability of the small time expansion of the heat kernel with a vector potential, providing explicit formulas and deriving a Poisson formula on the torus.

Contribution

It introduces a method to establish Borel summability for heat kernels with vector potentials and derives explicit formulas and a Poisson formula on the torus.

Findings

Established Borel summability of the heat kernel expansion

Derived an explicit formula for the heat kernel with vector potential

Obtained a Poisson formula on the torus

Abstract

We study the Borel summability of the small time expansion of the heat kernel associated to a first order perturbation of a Laplacian. An explicit formula for this kernel plays a central role. As a consequence, we get a Poisson formula on the torus.