Single-particle Green's function in the anisotropic Heisenberg model II. Allowance for higher correlation functions

The spectrum and damping of magnons is found on the basis of a self-consistent allowance for the dynamics and kinematics of the Pauli operators in an integral term of second order in the interaction. A generalized Tyablikov equation is obtained for the magnetization, this being applicable in the whole range of temperatures and fields and nat containing a term $T_3$ at small $T$. It is shown that the rigorous Dyson theory corresponds exactly to the approximation of the two-particle $T$ scattering matrix of the magnons (without allowance for bound states), so that the nonunitary Dyson–Maleev transformation to Bose operators becomes superfluous. Dyson's equations are generalized to the anisotropic case and a correction is found to the gap in the magnon spectrum.