Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalization Group Approach to Interacting Fermions   The stability of nonrelativistic fermionic systems to interactions is studied
within the Renormalization Group framework. A brief introduction to $\phi^4$
theory in four dimensions and the path integral formulation for fermions is
given. The strategy is as follows. First, the modes on either side of the Fermi
surface within a cut-off $\Lambda$ are chosen and a path integral is written to
describe them. An RG transformation which eliminates a part of these modes, but
preserves the action of the noninteracting system is identified. Finally the
possible perturbations of this free-field fixed point are classified as
relevant, irrelevant or marginal. A $d=1$ warmup calculation involving a system
of fermions shows how, in contrast to mean-field theory, the RG correctly
yields a scale invariant system (Luttinger liquid) In $d=2$ and 3, for
rotationally invariant Fermi surfaces, {\em automatically} leads to Landau's
Fermi liquid theory, which appears as a fixed point characterized by an
effective mass and a Landau function $F$, with the only relevant perturbations
being of the superconducting (BCS) type The functional flow equations for the
BCS couplings are derived and separated into an infinite number of flows, one
for each angular momentum. It is shown that similar results hold for
rotationally non-invariant (but time-reversal invariant) Fermi surfaces also, A
study of a nested Fermi surface shows an additional relevant flow leading to
charge density wave formation. For small $\Lambda / K_F$, a 1/N expansion
emerges, with $N = K_F/ \Lambda$, which explains why one is able to solve the
narrow cut-off theory. The search for non-Fermi liquids in $d=2$

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The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
16
The categories of this paper are: stat
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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom