Convergence of Perturbation Expansions in Fermionic Models. Part 1: Nonperturbative Bounds

TL;DR

This paper derives a nonperturbative bound on the operator norm of a fermionic renormalization group map, aiding the construction of Green's functions for a weakly coupled 2D fermion gas.

Contribution

It provides a new nonperturbative estimate for fermionic renormalization group maps, enabling better control over Green's functions in fermionic models.

Findings

Derived a strong operator norm estimate for fermionic RG maps

Controlled all but quartic contributions to Green's functions

Facilitated construction of thermodynamic Green's functions in 2D fermion gases

Abstract

An estimate on the operator norm of an abstract fermionic renormalization group map is derived. This abstract estimate is applied in another paper to construct the thermodynamic Green's functions of a two dimensional, weakly coupled fermion gas with an asymmetric Fermi curve. The estimate derived here is strong enough to control everything but the sum of all quartic contributions to the Green's functions.