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Conserving approximations are applied to the attractive Holstein and Hubbardmodels (on an infinite-dimensional hypercubic lattice). All effects ofnonconstant density of states and vertex corrections are taken into account inthe weak-coupling regime. Infinite summation of certain classes of diagramsturns out to be a quantitatively less accurate approximation than truncation ofthe conserving approximations to a finite order, but the infinite summationapproximations do show the correct qualitative behavior of generating a peak inthe transition temperature as the interaction strength increases.Comment: 33 pages, typeset in ReVTeX, NSF-ITP-94-0

Conserving approximations for the attractive Holstein and Hubbard models