Generalization and Interpretation of Dirac's Positive-Energy Relativistic Wave Equation

Abstract

We generalize Dirac's new equation so as to describe particles of mass $m$ and arbitrary spin $s$. The same remarkable properties are found: positive energy, non-negative density, a conserved four-vector current, and the impossibility of minimal electromagnetic interaction. We show that the particles described by a subset of these equations are composites of two subparticles interacting by a relativistic action-at-a-distance interaction characterized by two harmonic oscillators. For these composite particles we find a linear relation between the square of the mass and the spin. We emphasize that the essential content of the generalized new Dirac equation is that it constitutes an example of a convariant solution for two interacting particles, and provides an explicit example of a new quantal subdynamics distinct from the (classical) front relativistic dynamics of Dirac.