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 Padé 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 Padé method.
U. D. Jentschura et al., "Resummation of QED Perturbation Series by Sequence Transformations and the Prediction of Perturbative Coefficients," Physical Review Letters, vol. 85, no. 12, pp. 2446-2449, American Physical Society (APS), Sep 2000.
The definitive version is available at https://doi.org/10.1103/PhysRevLett.85.2446
Keywords and Phrases
Algorithms; Approximation Theory; Asymptotic Stability; Computational Complexity; Mathematical Transformations; Perturbation Techniques; Nonlinear Sequence Transformations; Pade Approximants; Wynn Epsilon Algorithms; Quantum Theory
International Standard Serial Number (ISSN)
Article - Journal
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