Neoclassical models of charged particles

Abstract

Classical electrodynamics (CED) has achieved great success in its domain of application, but despite this success, it has remained a theory that lacks complete self-consistency. It is worthwhile trying to make CED a self-consistent theory, because many important phenomena lie within its scope, and because modern field theories have been modelled on it. Alternative approaches to CED might help finding a definite formulation, and they might also lead to the prediction of new phenomena. Here we report two main results. The first one derives from standard CED. It is shown that the motion of a charged particle is ruled not only by the Lorentz equation, but also by equations that are formally identical to Maxwell equations. The latter hold for a velocity field and follow as a strict logical consequence of Hamilton's action principle for a \emph{single} particle. We construct a tensor with the velocity field in the same way as the electromagnetic tensor is constructed with the four potential. The two tensors are shown to be proportional to one another. As a consequence, and without leaving the realm of standard CED, one can envision new phenomena for a charged particle, which parallel those involving electromagnetic fields. The second result refers to a field-free approach to CED. This approach confirms the simultaneous validity of Maxwell-like and Lorentz equations as rulers of charged particle motion.