Tiered structure and symmetry of the electromagnetic equations

Abstract

The structure of Maxwell's equations is reproduced for the potentials introducing a second vector potential , in addition to the usual vector potential . These in turn can be described in terms of the so-called potpotentials and the process continued ad infinitum. A unified scheme is expounded, where the relationship between contiguous and alternate tiers is presented. The Heaviside Larmor (HL) symmetry is fulfilled in any one tier. In the presence of matter, the electric–magnetic symmetry is broken by electric monopoles but preserved for the electric and magnetic dipoles. The Hertz potentials will be shown to be the second tier potentials. The obtention of vector solutions from a scalar solution will be shown to be a direct consequence of linear superposition, the HL symmetry and the structure of the electromagnetic equations for all tiers. The Debye potentials provide such solutions for spherical symmetry. The physical reality of the quantities in any one tier is discussed, in particular regarding the question of gauge transformations and physical observables.