Faddeev–Jackiw Hamiltonian reduction for free and gauged Rarita–Schwinger theories

We study the Faddeev–Jackiw symplectic Hamiltonian reduction for 3 + 1 -dimensional free and Abelian gauged Rarita–Schwinger theories that comprise Grassmannian fermionic fields. We obtain the relevant fundamental brackets and find that they are in convenient forms for quantization. The brackets are independent of whether the theories contain mass or gauge fields, and the structures of constraints and symplectic potentials largely determine characteristic behaviors of the theories. We also note that, in contrast to the free massive theory, the Dirac field equations for free massless Rarita–Schwinger theory cannot be obtained in a covariant way.