Path-integrals in multiply-connected spaces and the Aharonov-Bohm effect

Abstract

The motion of a nonrelativistic charged particle in a plane, multiply-connected region is studied within the framework of Feynman's path-integral approach to quantum mechanics. In particular, the authors study the simple case when the multiply-connected region is obtained by excluding a disc from the plane. If a nonzero magnetic flux is confined inside the disc, this is shown to include a change in the one-dimensional unitary representation of the fundamental group of the space which enters a proper definition of the path-integral. In this way, a simple explanation of the Aharonov-Bohm effect is shown to arise.