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We analyze the Rarita--Schwinger (RS) massless theory in the Lagrangian andHamiltonian approaches. At the Lagrangian level, the standard gamma-trace gaugefixing constraint leaves a spin-1/2 and a spin-3/2 propagating Poincar\'e grouphelicities. At the Hamiltonian level, the result depends on whether the Diracconjecture--that all first class constraints generate gauge symmetries--isassumed or not. In the affirmative case, a secondary first class constraintmust be added to the total Hamiltonian and a corresponding gauge fixingcondition must be imposed, completely removing the spin-1/2 sector. In theopposite case, the spin-1/2 field propagates and the Hamilton field equationsmatch the Euler-Lagrange equations.

On the spin content of the classical massless Rarita--Schwinger system