Quantum states, symmetry and dynamics in degenerate spin s=1 magnets

The article deals with spin s=1 magnets. The symmetry conditions for normal and degenerate equilibrium states are defined and types of magnetic ordering found out. For each type of symmetry breaking the structure of source in the Gibbs statistical operator has been obtained and additional thermodynamic parameters introduced. The algebra of Poisson bracket for magnetic degrees of freedom has been established and nonlinear dynamic equations have been derived. Using the models of the exchange interaction, we have calculated the spectra of collective excitations for two degenerate states whose order parameters have digerent signature under the time reversal transformation.