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A Two Dimensional Fermi Liquid. Part 1: Overview

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Abstract

In a series of ten papers (see the flow chart at the end of §I), 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 space dimensions have nonzero radius of convergence. The models have ‘‘asymmetric’’ Fermi surfaces and short range interactions. One consequence of the convergence of the perturbation expansions is the existence of a discontinuity in the particle number density at the Fermi surface. Here, we present a self contained formulation of our main results and give an overview of the methods used to prove them.

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Authors and Affiliations

  1. Department of Mathematics, University of British, Columbia, Vancouver, B.C., Canada, V6T 1Z2

    Joel Feldman

  2. Mathematik, ETH-Zentrum, 8092 Zürich, Switzerland

    Horst Knörrer & Eugene Trubowitz

Authors
  1. Joel Feldman
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  2. Horst Knörrer
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  3. Eugene Trubowitz
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Correspondence to Joel Feldman.

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J.Z. Imbrie

Research supported in part by the Natural Sciences and Engineering Research Council of Canada and the Forschungsinstitut für Mathematik, ETH Zürich.

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Feldman, J., Knörrer, H. & Trubowitz, E. A Two Dimensional Fermi Liquid. Part 1: Overview. Commun. Math. Phys. 247, 1–47 (2004). https://doi.org/10.1007/s00220-003-0996-0

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