Gauge Symmetries and gauge trnasformations for Maxwell Equations

Abstract

In a previous publication [5] we introduced gauge invariant electromagnetic potentials. However the field equations that were derived for them turn out to be the Coulomb gauge field equations. This raises the question of the nature of these new gauge invariant potentials and its relations with Coulomb gauge potentials. In this paper we prove that this new potentials are in fact gauge invariant and identical with the Coulomb gauge potentials. In other words: the Coulomb gauge potentials are gauge invariant potentials that cannot be related to Lorenz gauge potentials because, contrary to current ideas, there is not anything like a gauge transformation relating both gauges.