Asymptotic Improvement of Resummation and Perturbative Predictions in Quantum Field Theory

Abstract

The improvement of resummation algorithms for divergent perturbative expansions in quantum field theory by asymptotic information about perturbative coefficients is investigated. Various asymptotically optimized resummation prescriptions are considered. The improvement of perturbative predictions beyond the reexpansion of rational approximants is discussed.

21 pages, LaTeX, 3 tables; title shortened; typographical errors corrected; minor changes of style; 2 references added

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Cited by in corpus (16)

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• ${\alpha }_s$ from $\tau$ decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion
• Numerical Evidence that the Perturbation Expansion for a Non-Hermitian $\mathcal{P}\mathcal{T}$-Symmetric Hamiltonian is Stieltjes
• Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field
• Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by Č\'ıžek, Zamastil, and Skála. I. Algebraic Theory
• QED Effective Action Revisited
• On the Analyticity of Laguerre Series
• Scale- and scheme-independent extension of Pade approximants; Bjorken polarized sum rule as an example
• (Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap
• Improved Conformal Mapping of the Borel Plane
• Nonlinear Sequence Transformations: Computational Tools for the Acceleration of Convergence and the Summation of Divergent Series
• Extended Comment on "One-Range Addition Theorems for Coulomb Interaction Potential and Its Derivatives" by I. I. Guseinov (Chem. Phys. Vol. 309 (2005), pp. 209 - 213)
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• A new determination of higher-order QCD corrections to hadronic $\tau$ decays
• Global Rational Approximations of Functions With Factorially Divergent Asymptotic Series