Single Scale Analysis of Many Fermion Systems Part 2: The First Scale

Abstract

Abstract. For a two dimensional, weakly coupled system of fermions at temperature zero, one principal ingredient used to control the composition of the associated renormalization group maps is the careful counting of the number of quartets of sectors that are consistent with conservation of momentum. A similar counting argument is made to show that particleparticle ladders are irrelevant in the case of an asymmetric Fermi curve.

Single Scale Analysis of Many Fermion Systems Part 3: Sectorized Norms

“…We shall later, in Lemma XVII.5 of [FKTo3], prove a general scale version. Let ρ m;n m,n∈IN 0 be a system of positive real numbers and X ∈ N d+1 with X 0 < 1.…”

“…Recall that Ant ext was introduced in Definition II.9 of [FKTo1]. Observe that the function on the left hand side is in F m+1 (n − 1).…”

“…A more careful argument in which one (see Definition XII.1 of [FKTo3] for the precise construction) • applies Proposition IV.8.i to obtain |||C (j)…”

A Two Dimensional Fermi Liquid. Part 1: Overview

“…For details, see Proposition XIII.1 and Lemma XIII.2 of [FKTo3]. Observe that, with sectorization, c…”

Convergence of Perturbation Expansions in Fermionic Models. Part 2: Overlapping Loops

“…For a short description, see subsection 4 of [FKTf1,§II]. In [FKTo3], we use nonperturbative bounds for systems, in two space dimensions, that are based on the cancellation scheme between diagrams developed in part 1 of this paper. In this second part, we modify the construction so that we can exploit enough overlapping loops to get improved power counting for the two point function and the non-ladder part of the four point function.…”