Field theory of the spinning electron: Internal motions

TL;DR

This paper develops a new classical field theory for the spinning electron, introducing a novel 4-velocity equation that clarifies internal zitterbewegung motions and their kinematic properties, differing from Dirac theory.

Contribution

It proposes a new classical 4-velocity field equation for the electron, providing a clearer description of internal motions and their kinematics, based on Barut-Zanghi theory.

Findings

Explicit description of internal zitterbewegung motions at different speeds

New kinematic properties of the velocity field

Different from Dirac theory's velocity description

Abstract

We present here a field theory of the spinning electron, by writing down a new equation for the 4-velocity field v^mu (different from that of Dirac theory), which allows a classically intelligible description of the electron. Moreover, we make explicit the noticeable kinematical properties of such velocity field (which also result different from the ordinary ones). At last, we analyze the internal zitterbewegung (zbw) motions, for both time-like and light-like speeds. We adopt in this paper the ordinary tensorial language. Our starting point is the Barut-Zanghi classical theory for the relativistic electron, which related spin with zbw. This paper is dedicated to the memory of Asim O. Barut, who so much contributed to clarifying very many fundamental issues of physics, and whose work constitutes a starting point of these articles.