Rarita-Schwinger equation from principle equation for all spins

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.