The structure of the plane waves for a spin 3/2 particle, massless case, gauge symmetry

The structure of plane wave solutions for a relativistic spin 3/2 particle described by a 16-component vector-bispinor is studied. In the massless case,two representations of the equation are used: in theRarita-Schwinger basis and in a special second basis in which the wave equation contains the Levi-Civita tensor. In this second basis, the existenceof trivial solutions in the form of a gradient on arbitrary bispinor becomes obvious. It is shown thatthe general solution of the massless equation consists of 6 linearly independent solutions. It is explicitly proved that four of them can be identifiedwith gauge solutions and, therefore, can be removedas non-physical. The exclusion procedure of gaugecomponents is carried out in both representations ofthe massless equation.