SU(2s+1) symmetry and nonlinear dynamic equations of spin s magnets

Abstract

The article is devoted to the description of dynamics of magnets with arbitrary spin on the basis of the Hamiltonian formalism. The relationship between the magnetic ordering and Poisson bracket subalgebras of the magnetic degrees of freedom for spin s=1/2; 1; 3/2 has been established. We have been obtained non-linear dynamic equations without damping for normal and degenerate non-equilibrium states of high-spin magnets with the properties of the SO(3), SU(4), SU(2)$\times$SU(2), SU(3), SO(4), SO(5) symmetry of exchange interaction. The connection between models of the magnetic exchange energy and the Casimir invariants has been discussed.