A functional-analytic construction of the stochastic parallel transport in Hermitian bundles over Riemannian manifolds

Abstract

This article presents a purely functional-analytic construction of the concept of stochastic parallel transport in Hermitian bundles over Riemannian manifolds. As a byproduct, we also obtain a form of the Feynman-Kac formula in vector bundles that is, to our best knowledge, the most general found so far.