Weak-coupling expansions (conserving approximations) are carried out for the attractive Holstein and Hubbard models (on an infinite-dimensional hypercubic lattice) that include all band-structure and vertex correction effects. Quantum fluctuations are found to renormalize transition temperatures by factors of order unity, but may be incorporated into the superconducting channel of Migdal-Eliashberg theory by renormalizing the phonon frequency and the interaction strength.

• Received 17 August 1993

DOI:https://doi.org/10.1103/PhysRevB.49.6368