Armando G. M. Neves
Perturbation theory for the Fermi liquids in d>1
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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.