Representations of the duals of gauge field tensors

Abstract

Classical electromagnetic fields admit a perfectly symmetrical description in terms of the electromagnetic field tensors and the duals thereof, this phenomenon being a simple consequence of Maxwell’s equations for free fields. Since the Yang–Mills equations for free gauge fields possess a somewhat analogous structure, the possibility of a similar symmetrical description of gauge fields is investigated. It is shown that source-free Yang–Mills equations do, in fact, imply the existence of a new gauge in terms of which the duals of the field tensors admit a representation; however, the latter does not in general possess a structure which is identical with that of the field tensors in terms of the original gauge.