Particle with spin S=3/2 in Riemannian space-time
arXiv:1109.3871
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, Ψ^{0}_{c} = \partial_{c} ψ. Generalization of that property for Riemannian model is performed; it is shown that in general covariant case solutions of the gradient type Ψ^{0}_β = (\nabla_β + Γ_β)Ψexist in space-time regions where the Ricci tensor obeys an identity R_{αβ} - {1 \over 2} R g_{αβ} = 0.
12 pages, 61 references, Chapter 7 in: V.M. Red'kov, Fields in Riemannian space and the Lorentz group (in Russian). Publishing House "Belarusian Science", Minsk, 2009