maynard's Journal: Curl-Free Vector Potential Effects in a Simply Connected

Full paper in PDF form (warning: very large pdf!)

"Curl-Free Vector Potential Effects in a Simply Connected Space"
Raymond C. Gelinas
Scanned from the 1986 Tesla Symposium

ABSTRACT:

A gauge invariant expression for the phase difference between two points of a wavefunction is derived using the Schrodinger equation for a charged particle in the presence of a vector potential. Such a phase difference is found to be the gauge invariant in a simply connected space in the quantum formalism. As applies to the Aharonov and Bohm effect, these findings therefore show that a multiply connected space is not an essential condition for establishing gauge invariance. That the Aharonov and Bohm experiements are constrained by a requirement for a multiply connected space, is a consequence of the properties of electron beams which cannot provide two separate sources of mutually phase coherent de Broglie waves. The macroscopic quantum interference properties of the superconducting Josephson junction are described. It is shown that a Josephson junction provides quantum interference between two mutually phase coherent souces of superconductive wavefunctions and therefore enables detection of curl-free vector potential effects in a simply connected space. An experiment is described to detect a change in phase difference of the superconductive wavefunction across a Josephson junction caused by a remote source of curl-free vector potential.