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

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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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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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Corresponding author

Correspondence to Joel Feldman.

Additional information

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. Convergence of Perturbation Expansions in Fermionic Models. Part 1: Nonperturbative Bounds. Commun. Math. Phys. 247, 195–242 (2004). https://doi.org/10.1007/s00220-004-1039-1

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  • DOI: https://doi.org/10.1007/s00220-004-1039-1

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