Eliashberg equations with momentum-dependent Kernels for the two-dimensional Hubbard model

We discuss the impact of the strong electron-phonon interactions on the physical properties of correlated electrons in the two-dimensional Hubbard model. An easy access to the physical properties of the superconducting state is obtained by solving the Eliashberg equations with explicit momentum-dependent kernels. In order to facilitate the numerical procedure to solve these equations, correlations are treated within the Gutzwiller approximation (i.e., mean-field-slave boson approximation). Our results strongly support the view thatd-wave symmetry is the most important feature of the superconducting state in the copper oxides. A possible extension beyond the mean field approximation is also presented.