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.