The wave-function description of the electromagnetic field
Abstract
For an arbitrary electromagnetic field, we define a prepotential , which is a complex-valued function of spacetime. The prepotential is a modification of the two scalar potential functions introduced by E. T. Whittaker. The prepotential is Lorentz covariant under a spin half representation. For a moving charge and any observer, we obtain a complex dimensionless scalar. The prepotential is a function of this dimensionless scalar. The prepotential of an arbitrary electromagnetic field is described as an integral over the charges generating the field. The Faraday vector at each point may be derived from by a convolution of the differential operator with the alpha matrices of Dirac. Some explicit examples will be calculated. We also present the Maxwell equations for the prepotential.
Cite
@article{arxiv.1305.5210,
title = {The wave-function description of the electromagnetic field},
author = {Yaakov Friedman},
journal= {arXiv preprint arXiv:1305.5210},
year = {2013}
}