General Gauge Invariance of Massive Electrodynamics and the Existence of a Massless Scalar Particle

Abstract

We have formulated a theory of massive electrodynamics which admits gauge invariance of the second kind. In so doing, a massless scalar field is needed. However, if the conserved-current condition ${\partial }_{\mu }{j}^{\mu }=0\mathrm{}$ is satisfied, this scalar field has no dynamical consequences. This theory then reduces to the conventional theory. When the conserved-current condition is not satisfied, a generalized current must still be conserved in order to have consistency of the theory. In an addendum, a brief discussion of the generalized Stueckelberg formulation is given.