Hamiltonian approach to the theory of antiferromagnetic systems

The dynamical equations of an antiferromagnetic are obtained in the exchange approximation in the framework of the Hamiltonian approach, and the differential conservation laws associated with the symmetries of the Hamiltonian system are studied. The general structure of infinitesimally small transformations that leave the Poisson brackets of the dynamical variables – the spin density $s_\alpha$ and the antiferromagnetism vector $l_\alpha$ invariant is found. The spectrum of spin waves is determined, and the lowfrequency asymptotic behavior of the Green's functions of arbitrary dynamical variablesa andb is obtained. The connection between the Hamiltonian and Lagrangian approaches to the theory of antiferromagnetic systems is established.