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

The paper deals with spin s=1 magnets. The symmetry conditions for normal and degenerate equilibrium states are defined and types of magnetic ordering were found out. For each type of symmetry breaking the structure of source in the Gibbs statistical operator has been obtained and additional thermodynamic parameters have been 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 different signatures under the time reversal transformation.