On the existence of superconductivity in the Hubbard model

A generalized Wick theorem is proposed for the superconducting phase of the single-band Hubbard model, and a thermodynamic diagram technique taking into account the strong electron correlations of the system is developed. An exact Dyson equation is obtained for the single-particle Green's function and an approximate equation for the correlation twoparticle Green's function. On this basis, a dynamical system of equations that determines the superconducting phase of the Hubbard model is formulated.