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 Feynman–Kac formula expressing solutions of the imaginary time Schrödinger equation as stochastic integrals.
A Feynman–Kac formula for magnetic monopoles