Massles Spin 3/2 Field, Spherical Solutions, Exclusion of the Gauge Degree of Freedom

Abstract

Covariant relativistic system for vector-bispinior describing a massless spin 3/2 field is studied in spherical coordinates and tetrad of Minkowski space. Presentation of the equation with the use of covariant Levi-Civita tensor exhibits existence of gauge solutions in the form of the covariant 4-gradient over arbitrary bispinor. Substitution for the main vector-bispinior assumes diagonalization of four operators: of energy, square and third projection of the total angular momentum, and space reflection. After separation of the variables, we derive radial system for eight independent functions. General structure of the spherical gauge solutions is specified, and it is demonstrated that the gauge 8 radial functions satisfy the derived system of 8 equations. It is proved that the general system reduces to two couples of independent 2-nd order and nonhomogeneous differential equations, their particular solutions may be found with the use of the gauge solutions of special form. The corresponding homogeneous equations turn out to have one the same form, and have three regular singularities and one irregular of the rank 2. Frobeniustypes solutions for this equation have been specified, and he structure in involved power series id studied. Six remaining radial functions may be straightforwardly found though the use of simple algebraic relations. By this method we have been constructed two types of solutions for the massless spin 3/2 field which do not contain gauge constituents.