Angular Momentum in Dirac's New Electrodynamics

Abstract

TYABJI¹ recently determined the canonical and symmetrical energy momentum tensors of Dirac's² new theory of electrodynamics. Tyabji used the conventional definition of the canonical energy momentum tensor and symmetrized this tensor in the traditional manner^3–5. The canonical tensor given by Tyabji can be written without the explicit appearance of the ξ and η variables, as follows : or The symmetrizing tensor¹, , is or (5) simply removes the unsymmetrical mixed term of (2) and adds the ‘matter’ contribution to the energy momentum tensor to yield¹ If (3) is added to (4), the canonical tensor contains the ‘matter’ term, and the symmetrizing tensor cancels the mixed last term of (3). λ is a scalar function of x_µ, and can be interpreted as the rest mass density of the streams of electrical charge.