A Scalar Representation of Electromagnetic Fields

It is shown that in a region which is free of currents and charges, any electromagnetic field may be rigorously derived from a single, generally complex, scalar wave function V(X, t). In terms of this function the momentum density g(x, t) and the energy density w(x, t) of the field may be defined in such a way that they are represented by expressions analogous to the formulae for the probability current and the probability density in quantum mechanics; in a homogeneous isotropic medium 1. g(x, t) =--