The derivation of electromagnetic fields from a basic wave-function

Abstract

1. Derivation of a Logarithmic Wave Function. - Electromagnetic fields may be derived from wave-functions in at least two ways that are analytically distinct. In the first place four wave-functions satisfying a divergence relation may be chosen as the components of a 4-vector and field-vectors derived from these four electromagnetic potentials in the usual way. The four potentials may in their turn be derived by differential operations from the components of a 6-vector whose components may be taken to be any six wave-functions. This method is a generalization of the well-known methods of Fitzgerald and Hertz;(1) it has the disadvantage that the wave-functions cannot be chosen arbitrarily if magnetic poles are to be excluded.