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 language | English (US) |
---|---|
Pages (from-to) | 261-263 |
Number of pages | 3 |
Journal | Journal of Mathematical Physics |
Volume | 21 |
Issue number | 2 |
DOIs | |
State | Published - 1979 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics