Two-spinor description of massive particles and relativistic spin projection operators

TL;DR

This paper develops a two-spinor formalism to describe massive particles of arbitrary spin, deriving explicit relativistic spin projection operators and generalizing them to higher dimensions, enhancing understanding of relativistic wave functions and propagators.

Contribution

It introduces a novel two-spinor approach to construct relativistic spin projection operators for particles of any spin, including generalizations to higher-dimensional spacetimes.

Findings

Explicit expressions for relativistic spin projection operators for integer and half-integer spins.

Wave functions satisfy Dirac-Pauli-Fierz equations automatically.

Generalizations of projection operators to dimensions D>2.

Abstract

On the basis of the Wigner unitary representations of the covering group ISL(2,C) of the Poincar\'{e} group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the Dirac-Pauli-Fierz equations. In the framework of the two-spinor formalism we construct spin-vectors of polarizations and obtain conditions that fix the corresponding relativistic spin projection operators (Behrends-Fronsdal projection operators). With the help of these conditions we find explicit expressions for relativistic spin projection operators for integer spins (Behrends-Fronsdal projection operators) and then find relativistic spin projection operators for half integer spins. These projection operators determine the nominators in the propagators of fields of relativistic particles. We deduce generalizations of the Behrends-Fronsdal projection operators for arbitrary space-time dimensions D>2.