An Extended Poincare Algebra for Linear Spinor Field Equations

TL;DR

This paper extends a spinor formalism to include momentum operators, develops unitary representations for these operators, and discusses their physical interpretations within a covariant, linear field equation framework.

Contribution

It introduces an extended Poincare algebra for arbitrary spins, incorporating momentum operators into the spinor formalism with new unitary representations.

Findings

Extended the spinor formalism to include momentum operators.

Developed unitary quantum representations for the extended algebra.

Provided physical interpretations for the new operators.

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 ${1 \over 2}$ systems. The general spinor formulation for arbitrary spins given in a previous paper is extended to include momentum operators. Unitary quantum mechanical representations are developed for these operators, and physical interpretations are suggested.