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

Thierry Harge (1)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

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.

Mots clés: heat kernel; quantum mechanics; vector potential; first order perturbation; semi-classical; Wigner-Kirkwood expansion; Borel summation; Poisson formula; Wiener integral; Feynman integral

Domaines: Physique mathématique [math-ph]

Thierry Harge. Borel summation of the small time expansion of the heat kernel with a vector potential. 2012. ⟨hal-00784186⟩