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A Two Dimensional Fermi Liquid. Part 2: Convergence
Joel Feldman, Horst Knoerrer, Eugene Trubowitz
Using results established in other papers in our series, we prove the existence of the infinite volume, temperature zero, thermodynamic Green's functions of a two dimensional, weak…
A Two Dimensional Fermi Liquid. Part 1: Overview
Joel Feldman, Horst Knoerrer, Eugene Trubowitz
In a series of ten papers, of which this is the first, we prove that the temperature zero renormalized perturbation expansions of a class of interacting many-fermion models in two…
Convergence of Perturbation Expansions in Fermionic Models. Part 2: Overlapping Loops
Joel Feldman, Horst Knoerrer, Eugene Trubowitz
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 dimensi…
Convergence of Perturbation Expansions in Fermionic Models. Part 1: Nonperturbative Bounds
Joel Feldman, Horst Knoerrer, Eugene Trubowitz
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 Gr…
Particle-Hole Ladders
Joel Feldman, Horst Knoerrer, Eugene Trubowitz
A self contained analysis demonstrates that the sum of all particle-hole ladder contributions for a two dimensional, weakly coupled fermion gas with a strictly convex Fermi curve a…
Single Scale Analysis of Many Fermion Systems. Part 3: Sectorized Norms
Joel Feldman, Horst Knoerrer, Eugene Trubowitz
The generic renormalization group map associated to a weakly coupled system of fermions at temperature zero is treated by supplementing the methods of Part 1. The interplay between…