Single-particle Green's function in an anisotropic Heisenberg model

It is shown that a number of first-order theories that are widely used in the quantum theory of a uniaxially anisotropic Heisenberg ferromagnet with spin $1/2$ can be obtained in a simple and unified manner on the basis of a formally exact solution of the equation of motion for the single-magnon Green's function. All these theories give a renormalization of the energy of Btoch magnons without allowance for damping and differ by the degree to which the dynamic and the kinematic interaction are allowed for in an estimate of the spectrum in the generalized Hartree–Fok approximation.