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

TL;DR

This paper refines estimates for fermionic models by incorporating overlapping momentum loop constraints, aiding in the analysis of Green's functions in weakly coupled two-dimensional fermion gases.

Contribution

It introduces improved bounds on perturbation expansions considering overlapping loops, advancing the understanding of fermionic models with convex Fermi surfaces.

Findings

Enhanced estimates for fermionic perturbation series

Application to control ladder contributions in Green's functions

Better understanding of overlapping loop effects in 2D fermion gases

Abstract

We improve on the abstract estimate obtained in Part 1 by assuming that there are constraints imposed by `overlapping momentum loops'. These constraints are active in a two dimensional, weakly coupled fermion gas with a strictly convex Fermi curve. The improved estimate is used in another paper to control everything but the sum of all ladder contributions to the thermodynamic Green's functions.