Single-particle Green's function in an anisotropic Heisenberg model. III. Spectrum and damping for anisotropy of the easy plane type

A study is made of the matrix Green's function constructed from Pauli operators similar to the one used in the theory of superfluidtty and superconductivity. The poles of the dynamical susceptibility and a renormalized spectrum of Bogolyubov-type magnons are found. General expressions are obtained for the normal and anomalous stngle-particle correlation functions and also an equation for the magnetization that generalizes Tyablikov theory. A canonical $u-v$-transformation is applied to the quasi-Bose operators in order to calculate the contribution of the integral term of second order to the energy shift and damping of magnons at low temperatures.