Green's functions of spiral magnets in the hydrodynamic and quasiparticle approximations

The influence of a weak external field on spiral magnets is investigated for a fairly general operator structure of the Hamiltonian of the interaction of the system with the external field. Equations of motion for the parameters of the reduced description are obtained, and the specific structure of the sources in these equations due to the external field is found. The asymptotic behaviors of the Green's functions $G_{ab}(k,\omega)$ are calculated for arbitrary quasilocal operators $\hat a$, $\hat b$ in the low-frequency region. A model of a weakly nonideal gas of magnons is investigated by means of the analogy between superfluid and magnetic systems with spiral structure. It is shown that the spectrum of elementary excitations of the spiral magnet arises due to the phenomenon of Bose condensation of spin waves. The Green's functions are found in the approximation of an ideal gas of quasiparticles. It is shown that the spectrum of a weakly nonideal gas of magnons goes over into a hydrodynamic spectrum if the internal energy is taken in the self-consistent field approximation.