Resummation of Nonalternating Divergent Perturbative Expansions

Abstract

A method for the resummation of nonalternating divergent perturbation series is described. The procedure constitutes a generalization of the Borel-Padé method. Of crucial importance is a special integration contour in the complex plane. Nonperturbative imaginary contributions can be inferred from the purely real perturbative coefficients. A connection is drawn from the quantum field theoretic problem of resummation to divergent perturbative expansions in other areas of physics.

5 pages, LaTeX, 2 tables, 1 figure; discussion of the Carleman criterion added; version to appear in Phys. Rev. D

Cited by in corpus (21)

• Multi-Instantons and Exact Results I: Conjectures, WKB Expansions, and Instanton Interactions
• From Useful Algorithms for Slowly Convergent Series to Physical Predictions Based on Divergent Perturbative Expansions
• Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Instantons in Quantum Mechanics and Resurgent Expansions
• Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field
• Asymptotic Improvement of Resummation and Perturbative Predictions in Quantum Field Theory
• Structure, Time Propagation and Dissipative Terms for Resonances
• Quantum Dot Potentials: Symanzik Scaling, Resurgent Expansions and Quantum Dynamics
• Improved Conformal Mapping of the Borel Plane
• Revisiting the Divergent Multipole Expansion of Atom-Surface Interactions: Hydrogen and Positronium, alpha-Quartz, and Physisorption
• Pade-related resummations of the pressure of quark-gluon plasma by approximate inclusion of g**6-terms
• Obtaining Bounds on The Sum of Divergent Series in Physics
• Calculation of the Characteristic Functions of Anharmonic Oscillators
• Distributional Borel Summability for Vacuum Polarization by an External Electric Field
• Enhanced and Generalized One-Step Neville Algorithm: Fractional Powers and Access to the Convergence Rate
• Optical asymptotics via Weniger transformation
• Asymptotic and factorial expansions of Euler series truncation errors via exponential polynomials
• From Divergent Series to Geometry: Resurgence of the Quantum Metric
• Joint use of the Weniger transformation and hyperasymptotics for accurate asymptotic evaluations of a class of saddle-point integrals. II. Higher-order transformations
• Global Rational Approximations of Functions With Factorially Divergent Asymptotic Series