Hydrodynamic spectrum of an antiferromagnet at low temperatures

An expression is obtained for the statistical operator $\rho_l$ describing the local-equilibrium state of a Heisenberg antiferromagnet during the hydrodynamic stage of evolution. This expression for $\rho_l$ is used to derive the hydrodynamic equations of an isotropic antiferromagnet and easy-axis and easy-plane models in the phase with noncollinear sublattices. For low temperatures, an explicit expression is found for the thermat corrections to the spectrum of long-wavelength excitations in a wide range of external magnetic field strengths.