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

TL;DR

This paper extends the analysis of fermion systems at zero temperature by addressing the unique challenges posed by the first renormalization group map without an ultraviolet cutoff, building on previous methods.

Contribution

It introduces methods to control the first RG map for weakly coupled fermions at zero temperature, where momentum components can be arbitrarily large.

Findings

Controlled the first RG map without ultraviolet cutoff

Extended previous methods to handle large momentum components

Provided a framework for analyzing fermion systems at zero temperature

Abstract

The first renormalization group map arising from the momentum space decomposition of a weakly coupled system of fermions at temperature zero differs from all subsequent maps. Namely, the component of momentum dual to temperature may be arbitrarily large - there is no ultraviolet cutoff. The methods of Part 1 are supplemented to control this special case.