Relating Rarita-Schwinger and Bargmann-Wigner Spin-3/2 Fields by Projection Technique

Projection operators relating trispinor representations to 5-tensor spinor representations of SO(5) representing spin-3/2 fields are explicitly constructed. Using these projection operators, we are able to analyze the structure of both totally symmetric and mixed symmetric trispinor fields, identifying 4-tensor spinors as the “base” sector of the totally symmetric Bargmann-Wigner field, and the Rarita-Schwinger 4-vector spinors as the “base” sector of mixed symmetric trispinors. The projectors allow us to derived connections relations that augment each base field with auxiliary components to completely specify the 5-tensor spinor representing each type of trispinor. These concepts were applied to obtain field equations and subsidiary equations by working only in the base sectors.