Gauge Invariance and the Lorentz Pondermotive Force

Abstract

In this paper it is shown that if one introduces into the Weyl theory of gauge invariance the two additional conditions that gauge (and therefore length), except for an arbitrary phase factor, be integrable along the path of a particle, and that the change in dimensions of a particle be a minimum, one immediately obtains the Lorentz pondermotive force for a charged particle in an electromagnetic field and the Bohr-Sommerfeld quantum integral.