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

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.

86 pages, 23 figures