96-627 Armando G. M. Neves
Renormalization group around a sphere for interacting fermion systems in d>1 (109K, LaTeX plus 6 appended eps figures, see instructions in the file) Nov 25, 96
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Abstract. We will sketch, see the companion paper "Perturbation theory for the Fermi liquids in d>1" for full details, a momentum-space renormalization group approach suited to a first-principles analysis, in perturbation theory, of interacting Fermi systems in more than one dimension. Our techniques are a momentum-space version of the ones introduced by Benfatto and Gallavotti cite{bg}, \cite{pr}, incorporating some important ideas by Shankar \cite{s}. A central role is played by bounds on contributions of certain Feynman graphs, substantially improving power counting ones. These bounds implement the important idea that renormalization is to be done around a surface in momentum space, rather than around a point, as usual. As a consequence of the improved bounds we can simplify the beta functional. Despite simplifications, the beta functional is still complicated and we cannot yet prove normality (Fermi liquid) or anomaly (non-Fermi liquid) of the system, but we think the formalism is a good starting point for further simplifications or numerical work.

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