Particle with spin S=3/2 in Riemannian space-time

Abstract

Equations for 16-component vector-bispinor field, originated from Rarita-Schwinger Lagrangian for spin 3/2 field extended to Riemannian space-time are investigated. Additional general covariant constrains for the field are produced, which for some space-time models greatly simplify original wave equation. Peculiarities in description of the massless spin 3/2 field are specified. In the flat Minkowski space for massless case there exist gauge invariance of the main wave equation, which reduces to possibility to produce a whole class of trivial solutions in the the form of 4-gradient of arbitrary (gauge) bispinor function, \Psi ^{0}_{c} = \partial_{c} \psi. Generalization of that property for Riemannian model is performed; it is shown that in general covariant case solutions of the gradient type \Psi^{0}_{\beta} = (\nabla_{\beta} + \Gamma_{\beta})\Psi exist in space-time regions where the Ricci tensor obeys an identity R_{\alpha \beta} - {1 \over 2} R g_{\alpha \beta} = 0.