Two-time Green's functions in superconductivity theory

Based on the method of the equations of motion for two-time Green's functions, we derive superconductivity equations for different types of interactions related to the scattering of electrons on phonons and spin fluctuations or caused by strong Coulomb correlations in the Hubbard model. We derive an exact Dyson equation for the matrix Green's function with the self-energy operator in the form of the multiparticle Green's function. Calculating the self-energy operator in the approximation of noncrossing diagrams leads to a closed system of equations corresponding to the Migdal–Eliashberg strong-coupling theory. We propose a theory of high-temperature superconductivity due to kinematic interaction in the Hubbard model. We show that two pairing channels occur in systems with a strong Coulomb correlation{:} one due to the antiferromagnetic exchange in interband hopping and the other due to the coupling to spin and charge fluctuations in hopping within one Hubbard band.