Improvement of Watson's theorem on Borel summability

Journal Article · Fri Feb 01 04:00:00 EST 1980 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.524408· OSTI ID:5541851

Sokal, A D

Watson's theorem, which gives sufficient conditions for Borel summability, is not optimal. Watson assumes analyticity and uniform asymptotic expansion in a sector vertical-barargzvertical-bar<..pi../2+epsilon, vertical-barzvertical-bar0; in fact, only the circular region Re(1/z) >1/R is required. In particular, one can take epsilon=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 phi/sub 2//sup 4/ quantum field theory.

• Research Organization: Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey 08544
• OSTI ID: 5541851
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 21:2; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

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658000 -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIELD THEORIES
FUNCTIONS
OPTIMIZATION
PERTURBATION THEORY
PHI4-FIELD THEORY
QUANTUM FIELD THEORY
SERIES EXPANSION