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On the Local Borel Transform of Perturbation Theory

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Abstract

We prove existence of the local Borel transform for the perturbative series of massive \({\varphi_4^4}\)-theory. As compared to previous proofs in the literature, the present bounds are much sharper as regards the dependence on external momenta, they are explicit in the number of external legs, and they are obtained quite simply through a judiciously chosen induction hypothesis applied to the Wegner-Wilson-Polchinski flow equations. We pay attention not to generate an astronomically large numerical constant for the inverse radius of convergence of the Borel transform.

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  1. Centre de Physique Théorique, CNRS, UMR 7644, Ecole Polytechnique, F-91128, Palaiseau, France

    Christoph Kopper

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  1. Christoph Kopper
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Correspondence to Christoph Kopper.

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Communicated by M. Salmhofer

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Kopper, C. On the Local Borel Transform of Perturbation Theory. Commun. Math. Phys. 295, 669–699 (2010). https://doi.org/10.1007/s00220-009-0979-x

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  • DOI: https://doi.org/10.1007/s00220-009-0979-x

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