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

2002/09/21 by Joel Feldman, Feldman, Joel, Horst Knoerrer +3
Mathematics · Physics and Astronomy · #82B28 (Primary) 81T08 (Secondary) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Chromodynamics and Particle Interactions #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:81T08 #msc:82B28

paper · pdf · doi:10.48550/arxiv.math-ph/0209045

58 pages, 2 figures

arxiv created 2002/09/21 · openalex publication_date 2002/09/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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