Covariant description of spin 1/2 particles in self--action

Abstract

The bispinor wave function finds its fundamental application in the study of electrons, neutrinos and protons as particles bound by their own potentials. Classical electromagnetism and the Dirac electron theory appear to be natural extensions of the physics that rules the electron itself. However, the charge density and the negative energy eigenvalues are two concepts which cannot survive further scrutiny. The electron and the proton resemble minute planetary systems where the bispinor terms defining their physical properties revolve with definite angular momentum around the singular point of the particles' potentials. The mass of the electron--neutrino in relation to the electron's and the mass of the latter in relation to the proton's are determined under particular assumptions. The most important feature of the new approach is the faithful representation of free particles at rest with respect to inertial systems of reference. This certainly enhances the foundation of physics; precisely in the realm of Quantum Mechanics, where the customary description of free electrons is a confusing consequence of the limited scope of the Schr\"{o}dinger and Dirac equations.