Armando G. M. Neves
Renormalization group around a sphere for interacting fermion systems in d>1
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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.