Spin and Zitterbewegung in a Field Theory of the Electron

摘要

In previous papers we investigated the classical theory of the electron spin, and its ”quantum” version, by using Clifford algebras; and we ended with a new non-linear Dirac-like equation (NDE). We re-address in this review the whole subject, and extend it, by adopting however the ordinary tensorial language, within the first quantization formalism. In particular, we re-derive the NDE for the electron field, showing it to be associated with a new conserved probability current. Incidentally, the Dirac equation results from the former by averaging over a Zbw cycle. Afterward, we derive an equation of motion for the 4-velocity field, which allows regarding the electron as an extended-like object with a classically intelligible internal structure. We carefully study the solutions of the NDE; with special attention to those implying (at the classical limit) light-like helical motions, since they appear to be the most adequate solutions for the electron description. At last we introduce a natural generalization of our approach, for the case in which an external electromagnetic potential is present.