The problem of summation over physical states in a theory of interacting spin waves

A new representation for the spin operators is suggested and on its basis the formalism involving both the rigorousness of diagram technique for the spin operators and the simplicity of diagram technique for the Fermi- and Bose-system is developed to calculate the Green's spin functions. This method is a basis for constructing a theory of high-frequency and thermodynamic properties of the magnetic ordered crystals and a systematic summation over physical states of interacting magnons at any temperatures.