Нерелятивистское приближение в 39-компонентной теории для частицы со спином 2

Abstract

The goal of the present paper is investigation of the nonrelativistic approximation in the 39-component theory for a spin 2 particle. We apply explicit expressions for four main matrices Γa with dimension 39×39 in the relevant first-order system of equations, written in Cartesian coordinates and in presence of external electromagnetic fields. For distinguishing the large and small constituents in the complete wave function, we apply three projective operators constructed on the base of the minimal polynomial of the 7-th order for the matrix Γ0. The relevant large and small components are found in explicit form. In each group, we have found independent variables; in particular, among the large components there exist only five independent ones. We have derived the nonrelativistic equation for 5-component wave function; it has the term describing interaction of the magnetic moment of the spin 2 particle with the external magnetic field we distinguished. This additional term is constructed by the projections of spin operator Si and the components of the magnetic field Bi.