Dirac's New Electrodynamics

Abstract

ABOUT twenty-five years ago, W. Gordon1, O. Klein2 and I3 shared in establishing a consistent set of field equations for a charge scalar ψ and the electromagnetic 4-potential Ak. To disencumber the formulæ, we take c Combining double low line 1 and take the Ak to mean the ordinary potentials multiplied by 2πe/h. Then the real Lagrangian density we used reads: with The asterisk means the complex conjugate, a comma ordinary differentiation, underlining the subsequent raising of the subscript; the metric is (- 1, - 1, - 1, 1); m is the reciprocal Compton wave-length of 'the particle'; ψ and Ak have the dimension reciprocal length; the allotment of indices is the customary (F14 Combining double low line Ex etc.), as opposed to the rational. From (1) and (2) one obtains the Euler equations: with the 4-current for which the equation of continuity follows from (4) and independently from (3). © 1952 Nature Publishing Group.