A Feynman-Kac formula for magnetic monopoles
Mathematical Physics
2021-02-16 v2 math.MP
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.
Cite
@article{arxiv.2005.09438,
title = {A Feynman-Kac formula for magnetic monopoles},
author = {J. Dimock},
journal= {arXiv preprint arXiv:2005.09438},
year = {2021}
}
Comments
19 pages