Nonlinear Phenomena in Complex Systems, 2024, Vol.27, No.1, pp.12

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2024, Vol.27, No.1, pp.12 - 36

Spin 2 Particle, Cylindric Symmetry, Projective Operator Method, External Magnetic Field

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

In the present paper we develop the theory of the massive spin 2 particle in presence of an external uniform magnetic field. We apply the matrix equation for spin 2 particle in Minkowski space-time, specifying it in cylindrical coordinates t, r, φ, z and tetrad formalism. By diagonalizing operators of the energy, the third projection of the total angular momentum, and the third projection of the linear momentum, we derive the system of 39 differential equations in polar coordinate r. In order to resolve this system we apply the method by Fedorov–Gronskiy based on the projective operator method. In accordance with this method, the dependance of all 39 functions is determined by only five different functions of the polar variable r, which belong to the hypergeometric type. We find in the explicit form five independent solutions of the basic matrix equation. For the energy values, we derived a 7-th order algebraic equation, it has been studied by numerical method; the physically interpretable energy values were separated.

Key words: spin 2 particle, matrix formalism, external magnetic field, projective operators, exact solutions, energy spectra

DOI: https://doi.org/10.5281//zenodo.10889593

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