The massless Rarita–Schwinger equation has a fermionic gauge symmetry: is invariant under the gauge transformation ψ ψ μ μ → → ψ ψ μ μ + ∂ ∂ μ μ ϵ ϵ , where ϵ ϵ ≡ ≡ ϵ ϵ α α is an arbitrary spinor field. This is simply the local supersymmetry of supergravity, and the field must be a gravitino.