Single-particle Green's function of a ferromagnet with single-ion anisotropy in the presence of a magnetic field of arbitrary direction

A general method of quantum-mechanical solution of the problem of the behavior of a ferromagnet with single-ion anisotropy in a magnetic field of arbitrary direction is developed. In it, the single-ion anisotropy is treated exactly and the exchange interaction in the random phase approximation. The method is based on preliminary implementation of unitary transformations of the Hamiltonian in the space of operators of the algebra of $SU(2S+1)$. The single-particle matrix Green's function constructed from Hubbard type operators for $S=1$ is studied. The spectrum of spin excitations, equations for the parameters of the transformations, and equations for the order parameters are constructed, and the ground state of the ferromagnet is determined more accurately.