Consistent quantization of massless fields of any spin and the generalized Maxwell's equations

Abstract

A simplified formalism of first quantized massless fields of any spin is presented. The angular momentum basis for particles of zero mass and finite spin s of the D(s-1/2,1/2) representation of the Lorentz group is used to describe the wavefunctions. The advantage of the formalism is that by equating to zero the s – 1 components of the wavefunctions, the 2s – 1 subsidiary conditions (needed to eliminate the non-forward and non-backward helicities) are automatically satisfied. Probability currents and Lagrangians are derived allowing a first quantized formalism. A simple procedure is derived for connecting the wavefunctions with potentials and gauge conditions. The spin 1 case is of particular interest and is described with the D(1/2,1/2) vector representation of the well known self-dual representation of the Maxwell's equations. This representation allows us to generalize Maxwell's equations by adding the E0 and B0 components to the electric and magnetic four-vectors. Restrictions on their existence are discussed.