Zero mass field with the spin 3/2: solutions of the wave equation and the helicity operator

The wave equation for the vector bispinor Ψa(x), which describes a zero mass spin 3/2 particle in the Rarita – schwinger form, is transformed into a new basis of Ψa(x), in which the gauge symmetry in the theory becomes evident: there exist solutions in the form of the 4-gradient of an arbitrary bispinor Ψa0(x) = ∂аΨ(x), For 16-component equation in this new basis, two independent solutions are constructed in explicit form, which do not contain any gauge constituents. Zero mass solutions are transformed into linear combinations of helicity states, the derived formulas contain the terms with all helicities σ = ±1/2, ±3/2.