Electromagnetic compensating gauge transformations

Abstract

Electromagnetic potentials have, in general, a smaller space-time symmetry than the corresponding fields. But to each symmetry element of the field a compensating gauge transformation can be found such that the combination of the two leaves the potential invariant. The same is true for the space-time symmetry of equations of motion of charged particles in external electromagnetic fields. Combining gauge with space-time transformations, one constructs symmetry groups of potentials and invariance operator groups of equations of motion. Their interrelation for arbitrary fields, in the classical and in the quantum-mechanical case, for relativistic and for non-relativistic symmetry transformations, are discussed. Potentials which differ only by a gauge transformation give rise to isomorphic invariance operator groups. The case of a linearly polarized transverse electromagnetic plane wave is briefly discussed.