Abstract
Relativistic system for a vector-bispinior describing a massless spin 3/2 field is studied in the spherical coordinates of Minkowski space. Presentation of the equation with the use of the covariant Levi-Civita tensor exhibits existence of the gauge solutions in the form of the covariant 4-gradient of an arbitrary bispinor. Substitution for 16-component field function is based on the use of Wigner functions, it assumes diagonalization of the operators of energy, square and third projection of the total angular momentum, and space reflection. We derive radial system for eight independent functions. General structure of the spherical gauge solutions is specified, and it is demonstrated that the gauge radial functions satisfy the derived system. 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. The corresponding homogeneous equations have one the same form, they have three regular singularities and one irregular of the rank 2. Frobenius types solutions for this equation have been constructed, and the structure of the involved power series with 4-term recurrent relations sre studied. Six remaining radial functions may be straightforwardly found by means of the simple algebraic relations. Thus, we have constructed two types of solutions with opposite parities which do not contain gauge constituents.
Highlights
The theory of spin 3/2 particle is attracted steady interest after the seminal investi gation by Pauli–Fierz [1; 2] and Rarita–Schwinger [3], this subject has a long history
In the present paper we examine the problem of spherical solutions for the 16-component system of equations describing a massless spin 3/2 particle in Minkowski space, we specify gauge solutions with spherical symmetry and construct solutions which do not contain the gauge components
The system of equations for the massless spin 3/2 field has been studied in the spherical coordinates of Minkowski space
Summary
The theory of spin 3/2 particle is attracted steady interest after the seminal investi gation by Pauli–Fierz [1; 2] and Rarita–Schwinger [3], this subject has a long history (see in [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]). A se parate interest has a massless case for spin 3/2 field, when as shown by Pauli and Fierz there exists specific gauge symmetry: the 4-gradient of arbitrary bispinor function provides us with solutions for the massless field equation for instance, see in [18]. Similar gauge symmetry arises for massless spin 2 theory referring to graviton. These gauge solutions do not contribute in physically observable quantities such as the energy and linear momentum. In the present paper we examine the problem of spherical solutions for the 16-component system of equations describing a massless spin 3/2 particle in Minkowski space, we specify gauge solutions with spherical symmetry and construct solutions which do not contain the gauge components. Substituting this gauge solution into eq (1), we obtain i 2 γ
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