Use of the Bogoliubov method of compensating “dangerous” diagrams to investigate magnetic superconductors

The gauge model in superconductivity theory describes a multiparticle dynamic system in a constant external field of the vector (electromagnetic) potential. The Hamiltonian of this dynamic system models a superconducting antiferromagnet and contains electron–boson interactions of the second (Fröhlich Hamiltonian) and fourth (exchange interaction) orders in the electron operators. This Hamiltonian accounts for the interaction of the magnetic moments of the conductance electrons. The bosonic spectrum of the system consists of normal modes of the coupled phonon–magnon oscillations. We obtain a system of equations describing a simultaneous compensation of the “dangerous” diagrams (those leading to energy divergence in the perturbation theory) corresponding to the creation of two (bivertex) or four (tetravertex) electron excitations from the vacuum. We find a solution of this system of equations corresponding to the superconducting state.