Rarita-Schwinger equation from principle equation for all spins

TL;DR

This paper derives the spin-3/2 Rarita-Schwinger equation from a principle equation based on Casimir eigenvalues, extending previous work on lower spins and revealing the structure of vector-spinor fields.

Contribution

It introduces a novel derivation of the Rarita-Schwinger equation from a unified principle, connecting all spins through Casimir eigenvalue equations.

Findings

Derived spin-3/2 Rarita-Schwinger equation from principle equations.

Showed vector-spinor fields contain two spin-1/2 Dirac fields.

Extended the framework to include all spins and helicities.

Abstract

In previous two articles we postulated that field equations for arbitrary spin and helicity are Casimir eigenvalue equations. In massive case, from such principle equation, we derived spin-$0$ Klein-Gordon, spin-$\frac{1}{2}$ Dirac and spin-$1$ vector equations. In the present article we will derived spin-$\frac{3}{2}$ Rarita-Schwinger equation, which is nontrivial combination of vector and spinor case. We will also show that vector-spinor field contains two spin-$\frac{1}{2}$ Dirac fields.