Electromagnetic Potential Vectors and the Lagrangian of a Charged Particle

Maxwells equations can be shown to imply the existence of two independent three-dimensional potential vectors. A comparison between the potential vectors and the electric and magnetic field vectors, using a spatial Fourier transformation, reveals six independent potential components but only four independent electromagnetic field components for each mode. Although the electromagnetic fields determined by Maxwells equations give a complete description of all possible classical electromagnetic phenomena, potential vectors contain more information and allow for a description of such quantum mechanical phenomena as the Aharonov-Bohm effect. A new result is that a charged particle Lagrangian written in terms of potential vectors automatically contains a spontaneous symmetry breaking potential.... Electrodynamics, Lagrangian field theory.