96-625 Armando G. M. Neves

Perturbation theory for the Fermi liquids in d>1 (107K, LaTeX plus 8 appended eps figures, see instructions in the file) Nov 25, 96

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Abstract. We develop a momentum space renormalization group formalism for the perturbative study of interacting Fermi systems in spatial dimensions greater than 1. We first prove improved bounds with respect to power counting for some Feynman graphs. These bounds show that among all graphs with 4 external legs, only some special ones, called direct and exchange graphs diverge, and they do so only at Cooper pairs or forward scattering configurations of external momenta. Using these bounds, we propose a novel renormalization scheme for the Fermi liquids, based on the physical idea of renormalizing only momentum configurations close (in a precise sense) to these.

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