Conformal and Uniformizing Maps in Borel Analysis

Abstract

Perturbative expansions in physical applications are generically divergent, and their physical content can be studied using Borel analysis. Given just a finite number of terms of such an expansion, this input data can be analyzed in different ways, leading to vastly different precision for the extrapolation of the expansion parameter away from its original asymptotic regime. Here we describe how conformal maps and uniformizing maps can be used, in conjunction with Pad'e approximants, to increase the precision of the information that can be extracted from a finite amount of perturbative input data. We also summarize results from the physical interpretation of Pad'e approximations in terms of electrostatic potential theory.

15 pages, 10 figures

References in corpus (1)

• $\lambda {\varphi }^4$ Theory II: The Broken Phase Beyond NNNN(NNNN)LO

Cited by in corpus (15)

• Uniformization and Constructive Analytic Continuation of Taylor Series
• Hydrodynamic Attractors in Ultrarelativistic Nuclear Collisions
• Exact multi-instantons in topological string theory
• Uniformizing Lee-Yang Singularities
• Probing the singularities of the Landau-gauge gluon and ghost propagators with rational approximants
• Exploring Lee-Yang and Fisher Zeros in the 2D Ising model through multipoint Padé approximants
• Higher-order QCD corrections to $H\to b\bar{b}$ from rational approximants
• Resurgence of the Effective Action in Inhomogeneous Fields
• Contribution to understanding the phase structure of strong interaction matter: Lee-Yang edge singularities from lattice QCD
• Resurgence of the Tilted Cusp Anomalous Dimension
• Reduction of Order and Transseries Structure of Radiation Reaction
• Noise Effects on Pade Approximants and Conformal Maps
• Introductory Lectures on Resurgence: CERN Summer School 2024
• Classical Weight-Four L-value Ratios as Sums of Calabi--Yau Invariants
• Model-independent extrapolation of MUonE data with Padé and D-Log approximants