Semi Classical Equations of Motion for Anti-Ferromagnetic System with Use of Coherent States in SU(1,1) Group

In this paper, the formulation of spin coherent state in the real parameter in SU(1,1) group is studied. This representation of the coherent state is used for measuring the integral path and its classical consequence in the physical system. Using the completeness relation of the coherent state, we derive a path integral expression for transition amplitude and in the classical limit, we solve the classical equation of motion. Then, Lagrangian, equations and dispersion relation describing one-dimensional exchange anisotropic Non-Heisenberg model in the Anti-ferromagnetic system for dipole branch are calculated.