A Feynman-Kac formula for magnetic monopoles

Abstract

We consider the quantum mechanics of a charged particle in the presence of Dirac's magnetic monopole. Wave functions are sections of a complex line bundle and the magnetic potential is a connection on the bundle. We use a continuum eigenfunction expansion to find an invariant domain of essential self-adjointness for the Hamiltonian. This leads to a proof of the a Feynman-Kac formula expressing solutions of the imaginary time Schrodinger equation as stochastic integrals.