Three-Body Scattering Theory of Correlated Hole and Electron States

We describe a theoretical scheme for the determination of quasiparticle spectra starting from the energy band structure of a metal and treating the on-site Hubbard repulsion beyond the mean-field theory. The method relies upon an expansion of the many-body states in terms of uncorrelated states with a different number of electron-hole pairs. By truncating the expansion to include configurations with one or two pairs one can achieve approximate expressions of the electron and hole self-energies. The interparticle scattering matrices appearing in such expressions are conveniently calculated using the Faddeev approach. Calculations performed for a constant density of states allow us to illustrate the role of three-body correlations in the metal-insulator transitions.