Linear Spinor Field Equations for Arbitrary Spins

TL;DR

This paper develops a covariant, linear spinor field equation framework for arbitrary spins by extending the Lorentz algebra, generalizing the Dirac formalism beyond spin-½ and spin-1 fields.

Contribution

It introduces a minimal extension of the Lorentz algebra to formulate covariant, linear field equations for arbitrary spins, explicitly demonstrating the matrix forms for spin ½ and 1.

Findings

Generalized Dirac matrices for arbitrary spins are constructed.

Explicit matrix forms are provided for spin ½ and spin 1 fields.

The formalism facilitates relativistic scattering calculations.

Abstract

When utilizing a cluster decomposible relativistic scattering formalism, it is most convenient that the covariant field equations take on a linear form with respect to the energy and momentum dispersion on the fields in the manner given by the Dirac form for spin \half systems. A general spinor formulation is given for arbitrary spins by minimally extending the Lorentz algebra to include operators whose matrix representation give general Dirac matrices. The forms of these matrices are explicitly demonstrated for spin \half and spin 1 fields.