A Simple Method to Make Asymptotic Series of Feynman Diagrams Converge

Details A Simple Method to Make Asymptotic Series of Feynman Diagrams Converge A Simple Method to Make Asymptotic Series of Feynman Diagrams Converge

2001-03-16

arxiv.org/abs/hep-th/0103134v3

Phys.Rev.Lett. 88 (2002) 141601

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, 7 figs., uses revtex; contains a discussion of the double-well

Scientific paper

10.1103/PhysRevLett.88.141601

We show that for two non-trivial lambda phi ^4 problems (the anharmonic oscillator and the Landau-Ginzburg hierarchical model), improved perturbative series can be obtained by cutting off the large field contributions. The modified series converge to values exponentially close to the exact ones. For lambda larger than some critical value, the method outperforms Pade's approximants and Borel summations. The method can also be used for series which are not Borel summable such as the double-well potential series. We show that semi-classical methods can be used to calculate the modified Feynman rules, estimate the error and optimize the field cutoff.

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