Massive particle spin 3/2 propagator

In the literature, massive particle with spin 3/2 propagator is explained by many models. However, the common model used in most studies is the Rarita-Schwinger one. Based on an inhomogenous Lorentz group theory, angular momentum (J) of a particle is coupled with boost generator (K). J and K can be decoupled by defining a new pair of generators, A and B with notation (A, B). Rarita-Schwinger representation is a tensor product of the vector (1/2, 1/2) representation and the Dirac (1/2, 0) ⊕ (0, 1/2) representation. This tensor product gives a spinor-vector representation. In other way, massive particle with spin 3/2 may have the (3/2, 0) ⊕ (0, 3/2) representation. This paper examines the difference between (1/2, 1/2) ⊗ [(1/2, 0) ⊕ (0, 1/2)] and (3/2, 0) ⊕ (0, 3/2) representations of masive spin 3/2 propagator.