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

TL;DR

This paper introduces a nonlinear sequence transformation method for resumming divergent QED perturbation series, which outperforms Padé approximants and can predict higher-order coefficients with improved accuracy.

Contribution

The authors develop a novel nonlinear sequence transformation technique that enhances resummation of divergent series and accurately predicts perturbative coefficients in quantum electrodynamics.

Findings

Outperforms Padé approximants in alternating series

Accurately predicts higher-order perturbative coefficients

Provides improved resummation of divergent series

Abstract

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.