Vertex corrections in the gap equation for high-temperature superconductors

We show that the Migdal theorem is obviously violated in the high-T-c super conductors and vertex corrections should be included, in particular, in the gap equation, in order to be consistent with the anomalously strong inelas tic scattering in the region of the "hot spots," which is observed from var ious experiments in the normal state of the high-T-c cuprates. The full ver tex correction is obtained nonperturbatively by utilizing the generalized W ard identity, which is shown to hold in the most important scattering chann el of the pairing interaction in the high-T-c cuprates. As a result, we fin d a strong enhancement of T-c from vertex corrections, against the strong p air breaking effect due to inelastic scattering. Our results, however, are most relevant for the optimally doped high-T-c cuprates, where the hot spot regions are well developed. [S0163-1829(99)05933-0].