Complex representation theory of the electromagnetic field

Abstract

A concise discussion of the 3-dimensional irreducible (1,0) and (0,1) representations of the restricted Lorentz group and their application to the description of the electromagnetic field is given. It is shown that a mass term is in conflict with relativistic invariance of a formalism using electric and magnetic fields only, contrasting the case of the two-component Majorana field equations. An important difference between the Dirac equation and the Dirac form of Maxwell's equations is highlighted by considering the coupling of the electromagnetic field to the electric current.