WEAK-COUPLING EXPANSIONS FOR THE ATTRACTIVE HOLSTEIN AND HUBBARD MODELS

Weak-coupling expansions (conserving approximations) are carried out f or the attractive Holstein and Hubbard models (on an infinite-dimensio nal hypercubic lattice) that include all band-structure and vertex cor rection effects. Quantum fluctuations are found to renormalize transit ion temperatures by factors of order unity, but may be incorporated in to the superconducting channel of Migdal-Eliashberg theory by renormal izing the phonon frequency and the interaction strength.