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

TL;DR

This paper develops a purely functional-analytic method to construct stochastic parallel transport in Hermitian bundles over Riemannian manifolds, leading to a generalized Feynman-Kac formula in vector bundles.

Contribution

It introduces a novel functional-analytic approach to stochastic parallel transport, extending the Feynman-Kac formula to the most general vector bundle setting known.

Findings

A new functional-analytic construction of stochastic parallel transport.

Derivation of a generalized Feynman-Kac formula for vector bundles.

Potential applications in geometric analysis and mathematical physics.

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.