### 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 φ_{2}^{4} quantum field theory.

Original language | English (US) |
---|---|

Pages (from-to) | 261-263 |

Number of pages | 3 |

Journal | Journal of Mathematical Physics |

Volume | 21 |

Issue number | 2 |

State | Published - 1979 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*21*(2), 261-263.

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

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 21, no. 2, pp. 261-263.

}

TY - JOUR

T1 - An improvement of Watson's theorem on Borel summability

AU - Sokal, Alan D.

PY - 1979

Y1 - 1979

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=4444361922&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4444361922&partnerID=8YFLogxK

M3 - Article

VL - 21

SP - 261

EP - 263

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 2

ER -