Spin 3/2 massless field, solutions with cylindrical symmetry, eliminating the gauge degrees of freedom

The system of equations for the vector-bispinor describing a spin 3/2 massless particle, is solved in cylindric coordinates of the Minkowski space. The covariant tetrad formalism is applied. Three operators, $i\partial_t$, $J_3$, $i\partial_z$ are diagonalized on the constructed solutions. After separating the variables, the system of 16 functions in the variable $r$ is derived. It is shown that the gauge solutions with cylindric symmetry, which are specified according to the Pauli–Fierz theory, satisfy these 16 equations identically. There are constructed 6 linearly independent solutions. Four of them coincide with the gauge ones, and two remain solutions do not contain the gauge degrees of freedom. These two solutions are expressed in terms of Bessel functions.