Resummation of QED Perturbation Series by Sequence Transformations and the Prediction of Perturbative Coefficients

Details Resummation of QED Perturbation Series by Sequence Transformations and the Prediction of Perturbative Coefficients Resummation of QED Perturbation Series by Sequence Transformations and the Prediction of Perturbative Coefficients

1999-11-08

arxiv.org/abs/hep-ph/9911265v2

Phys.Rev.Lett. 85 (2000) 2446-2449

Physics

High Energy Physics

High Energy Physics - Phenomenology

4 pages, LaTeX, 3 tables; minor adjustments

Scientific paper

10.1103/PhysRevLett.85.2446

We propose a method for the resummation of divergent perturbative expansions in quantum electrodynamics and related field theories. The method is based on a nonlinear sequence transformation and uses as input data only the numerical values of a finite number of perturbative coefficients. The results obtained in this way are for alternating series superior to those obtained using Pad\'{e} approximants. The nonlinear sequence transformation fulfills an accuracy-through-order relation and can be used to predict perturbative coefficients. In many cases, these predictions are closer to available analytic results than predictions obtained using the Pad\'{e} method.

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