An improvement of Watson's theorem on Borel summability

Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    Watson's theorem, which gives sufficient conditions for Borel summability, is not optimal. Watson assumes analyticity and uniform asymptotic expansion in a sector |argz|<π/2 + ε, |z| < R, with ε > 0; in fact, only the circular region Re(1/z) > 1/R is required. In particular, one can take ε = 0. This improved theorem gives a necessary and sufficient characterization of a large class of Borel-summable functions. I apply it to the perturbation expansion in the φ24 quantum field theory.

    Original languageEnglish (US)
    Pages (from-to)261-263
    Number of pages3
    JournalJournal of Mathematical Physics
    Volume21
    Issue number2
    StatePublished - 1979

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    Borel Summability
    theorems
    Uniform Asymptotic Expansion
    Borel Functions
    expansion
    Perturbation Expansion
    Analyticity
    Quantum Field Theory
    Theorem
    Sector
    sectors
    Sufficient
    perturbation
    Necessary
    Sufficient Conditions

    ASJC Scopus subject areas

    • Organic Chemistry

    Cite this

    An improvement of Watson's theorem on Borel summability. / Sokal, Alan D.

    In: Journal of Mathematical Physics, Vol. 21, No. 2, 1979, p. 261-263.

    Research output: Contribution to journalArticle

    Sokal, Alan D. / An improvement of Watson's theorem on Borel summability. In: Journal of Mathematical Physics. 1979 ; Vol. 21, No. 2. pp. 261-263.
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