Abstract
A unified complex model of Maxwell's equations is presented. The wave nature of the electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities. A new vacuum solution is obtained, and a new transformation under which Maxwell's equations are invariant is proposed. This transformation extends ordinary gauge transformation to include charge-current as well as scalar-vector potential. An electric dipole moment is found to be related to the magnetic charges, and Dirac's quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges. We generalize Maxwell's equations to include longitudinal waves. A formal analogy between this formulation and Dirac's equation is also discussed.