Symmetry of a magnet and structure of spin-wave Hamiltonian

General study of the structure of Hamiltonian of magnetic with the degenerate aground state is performed. It is shown that in the representation, in which the transition from one type of vacuum to another corresponds to the spin-wave Bose condensation, spectrum and amplitudes of quasiparticle interaction satisfy a number of relations, which characterize their structure in the region of small wave vectors. In particular, at least one activation-free mode was proved to exist in the spectrum of such a magnetic.