  We analyze the Rarita--Schwinger (RS) massless theory in the Lagrangian and
Hamiltonian approaches. At the Lagrangian level, the standard gamma-trace gauge
fixing constraint leaves a spin-1/2 and a spin-3/2 propagating Poincar\'e group
helicities. At the Hamiltonian level, the result depends on whether the Dirac
conjecture--that all first class constraints generate gauge symmetries--is
assumed or not. In the affirmative case, a secondary first class constraint
must be added to the total Hamiltonian and a corresponding gauge fixing
condition must be imposed, completely removing the spin-1/2 sector. In the
opposite case, the spin-1/2 field propagates and the Hamilton field equations
match the Euler-Lagrange equations.
