Pertubation theory around nonnested fermi surfaces. I. Keeping the fermi surface fixed

Abstract

The perturbation expansion for a general class of many-fermion systems with a nonnested, nonspherical Fermi surface is renormalized to all orders. In the limit as the infrared cutoff is removed, the counterterms converge to a finite limit which is differentiable in the band structure. The map from the renormalized to the bare band structure is shown to be locally injective. A new classification of graphs as overlapping or nonoverlapping is given, and improved power counting bounds are derived from it. They imply that the only subgraphs that can generater factorials in ther th order of the renormalized perturbation series are indeed the ladder graphs and thus give a precise sense to the statement that “ladders are the most divergent diagrams.” Our results apply directly to the Hubbard model at any filling except for half-filling. The half-filled Hubbard model is treated in another place.