On a representation for spin operators and its use in the theory of magnetism

A new representation is proposed which makes it possible to go from spin operators to some Bose operators. Transformation properties of these operators under rotations of the coordinate system are similar to transformation properties of the phonon operators under translations of the coordinate system. This makes it possible to take explicitly into account the symmetry of the Hamiltonian of interacting spin waves in all orders with respect to the interaction Hamiltonian. Explicit expression for the Hamiltonian of interacting spin waves in the long-wave limit is also found.