Conservation laws in the Dirac theory

Abstract

It is well known that the Dirac equations determine three conservation laws, for current, for energy momentum, and for angular momentum. Dividing the Dirac equations in two parts, one, DI, which does not contain the density ρ, the other, DII, which contains ρ, it is shown that DI together with the three conservation equations, determine DII. From this result, a model of formulation of the Dirac theory is proposed, following a scheme similar to that of classical mechanics, in which principles regarding the motion of one particle are associated with conservation theorems concerning statistical ensembles of particles.