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On the large order behavior of Φ 44

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Abstract

We continue the rigorous study of the large order behavior of the perturbation series for the ϕ4 model in 4 dimensions started in [1]. In this paper we prove a result announced in [1]. We show that the exact radius of convergence of the Borel transform of the renormalized perturbation series for ϕ 44 is greater than or equal to the expected value given by the position of the first “renormalon” [2]. This result holds for any vector (ϕ2)2 model withN components, and makes use of the “Lipatov bound” of [1]. This result is based on a partial resummation of counterterms similar to the one of [3], but in a phase-space analysis of the renormalized series.

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Author notes

  1. J. Feldman

    Present address: Mathematics Department, University of British Columbia, V6T 1Y4, Vancouver, B.C., Canada

Authors and Affiliations

  1. Service de Physique Théorique, CEA-Saclay, F-91191, Gif-sur-Yvette Cedex, France

    F. David

  2. Zentrum für theoretische Studien, ETH-Hönggerberg, CH-8093, Zürich, Switzerland

    J. Feldman

  3. Centre de Physique Théorique, Ecole Polytechnique, F-91128, Palaiseau Cedex, France

    V. Rivasseau

Authors
  1. F. David
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  2. J. Feldman
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  3. V. Rivasseau
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Communicated by K. Gawedzki

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David, F., Feldman, J. & Rivasseau, V. On the large order behavior of Φ 44 . Commun.Math. Phys. 116, 215–233 (1988). https://doi.org/10.1007/BF01225256

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  • DOI: https://doi.org/10.1007/BF01225256

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