  The method of equations of motion for spin operators in the case of O(3)
Heisenberg ferromagnet is systematically analyzed starting from the effective
Lagrangian. It is shown that the random phase approximation and the Callen
approximation can be understood in terms of perturbation theory for type B
magnons. Also, the second order approximation of Kondo and Yamaji for one
dimensional ferromagnet is reduced to the perturbation theory for type A
magnons. An emphasis is put on the physical picture, i.e. on magnon-magnon
interactions and symmetries of the Heisenberg model. Calculations demonstrate
that all three approximations differ in manner in which the magnon-magnon
interactions arising from the Wess-Zumino term are treated, from where specific
features and limitations of each of them can be deduced.
