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

TL;DR

This paper introduces a simplified first quantized formalism for massless fields of any spin, automatically satisfying subsidiary conditions and generalizing Maxwell's equations by incorporating additional scalar components.

Contribution

It presents a novel formalism that simplifies the description of massless fields of any spin and extends Maxwell's equations with new scalar components.

Findings

Automatically satisfies subsidiary conditions for massless fields

Connects wave functions with potentials and gauge conditions

Generalizes Maxwell's equations with additional scalar components

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 wave functions, 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 wave functions 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 E_0 and B_0 components to the electric and magnetic four-vectors. Restrictions on their existence are discussed.