What gauges can be used in applied electromagnetic calculations?

Abstract

In the classical electrodynamics, different gauges, i.e. connections between the electromagnetic potentials, are used. Some of these are quite specific and intended for calculations in special systems (absence of free charges, etc.). All of these specific gauges are reductions of the Lorenz gauge. However, in addition to this gauge, two more, i.e., the Coulomb and velocity gauges, can be used to describe systems of charges and currents without any restrictions. It is commonly accepted opinion that these three gauges are equivalent, meaning that the expressions for electromagnetic fields obtained from the potentials defined in these gauges are identical. However, it can be shown that the Coulomb and velocity gauges yield solutions corresponding to `superluminal propagation' of the electric field. Since such a propagation of the electric field has not been observed experimentally and, moreover, is forbidden by special relativity, it can be concluded that calculations in these gauges may yield incorrect results. Therefore, these gauges cannot be used in applied electromagnetic calculations.