Rarita-Schwinger equation from principle equation for all spins

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.