HAMILTONIAN APPROACH TO THE THEORY OF ANTIFERROMAGNETIC SYSTEMS

The dynamical equations of an antiferromagnetic are obtained in the ex change 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 infinites imally small transformations that leave the Poisson brackets of the dy namical variables - the spin density s(alpha) and the antiferromagneti sm vector l(alpha) - invariant is found. The spectrum of spin waves is determined, and the low-frequency asymptotic behavior of the Green's functions of arbitrary dynamical variables a and b is obtained. The co nnection between the Hamiltonian and Lagrangian approaches to the theo ry of antiferromagnetic systems is established.