Dirac and Maxwell’s Equations Derived from the Density Functions

Abstract

We present linear transformations between the components of the electric and magnetic fields, E = F1 (H ) and H = F2 (E ), which leave the expression for the density of electromagnetic field energy unchanged. If the coefficients occurring in these transformations are interpreted as the components of the momentum vector of the photon and use is made of the correspondence principle W →∂t and p→∂x, then these transformations turn out to be Maxwell’s equations. In a similar fashion, when starting from the probability density associated with the Dirac wave function, then one can also arrive, via appropriate transformations between the components of the 4- spinor, at the Dirac equation.