Projection Operator Method

Abstract

A general projection operator method in the equation of motion method for the two-time Green functions is formulated. An exact Dyson equation for an arbitrary Green function is derived. The method is used to consider the single-particle electron Green functions for the Hubbard model within the non-crossing approximation for the self-energy. Strong-coupling superconductivity theory for the model is formulated and an equation for the superconducting Tc is analyzed. We argue that the d-wave pairing with high-Tc can occur in the repulsive Hubbard model, which is mediated by the antiferromagnetic exchange interaction and the spin-fluctuation scattering, both induced by the kinematic interaction for the Hubbard operators. A microscopic theory for the dynamic spin susceptibility within the projection operator method is formulated. The theory is applied to study spin-excitation spectrum for the t–J model within the mode-coupling approximation for the self-energy. A new approach to the theory of the magnetic resonance mode in cuprate superconductors is proposed.