Nonlinear Phenomena in Complex Systems, 2025, Vol.28, No.3, pp.220

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2025, Vol.28, No.3, pp.220 - 241

Spin 2 Particle Theory, the Nonrelativistic Approximation

A. V. Ivashkevich, A. V. Bury, E. M. Ovsiyuk, V. V. Kisel, and V. M. Red'kov

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 Γ^a with dimension 39×39 in the relevant first order system of equations, written in Cartesian coordinates and in the presence of external an electromagnetic field. For distinguishing the large and small parts in the complete wave function, we use 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. Among them 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; in which term describing interaction of the magnetic moment of the spin 2 particle with the external magnetic field is separated.

Key words: spin 2 particle, the non-relativistic approximation, external electromagnetic fields, projective operators

DOI: https://doi.org/10.5281/zenodo.17237053

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