Physical Resurgent Extrapolation

Abstract

Expansions of physical functions are controlled by their singularities, which have special structure because they themselves are physical, corresponding to instantons, caustics or saddle configurations. Resurgent asymptotics formalizes this idea mathematically, and leads to significantly more powerful extrapolation methods to extract physical information from a finite number of terms of an expansion, including precise decoding of non-perturbative effects.

11 pages, 8 figures

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• High-precision numerical solution of the Fermi polaron problem and large-order behavior of its diagrammatic series
• Sets of Minimal Capacity and Extremal Domains
• Mapping the phase diagram of strongly interacting matter
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• Hydrodynamic Attractors in Ultrarelativistic Nuclear Collisions
• Conformal and Uniformizing Maps in Borel Analysis
• On the Higher Loop Euler-Heisenberg Trans-Series Structure
• New renormalons from analytic trans-series
• Nonlinear trident in the high-energy limit: Nonlocality, Coulomb field and resummations
• Existence of real time quantum path integrals
• Resonant resurgent asymptotics from quantum field theory
• Reduction of order, resummation and radiation reaction
• Resummation of quantum radiation reaction and induced polarization
• Gibbs entropy from entanglement in electric quenches
• Uniformizing Lee-Yang Singularities
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
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• Resurgence of the QCD Adler function
• Thermal and hard scales in transverse momentum distributions, fluctuations and entanglement
• Instantons, renormalons and the theta angle in integrable sigma models
• Soft and hard scales of the transverse momentum distribution in the Color String Percolation Model
• Integrated correlators at strong coupling in an orbifold of $\mathcal{N}=4$ SYM
• Self-similar extrapolation in quantum field theory
• Wilson loop correlators at strong coupling in $\mathcal{N}=2$ quiver gauge theories
• Renormalons beyond the Borel plane
• Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseux
• Resurgence of the Effective Action in Inhomogeneous Fields
• Defect correlators in a $\mathcal{N}=2$ SCFT at strong coupling
• The analytic structure of the fixed charge expansion
• Resurgent Analysis of Ward-Schwinger-Dyson Equations
• Resurgence of the Tilted Cusp Anomalous Dimension
• The QCD Adler function and the muon $g-2$ anomaly from renormalons
• Reduction of Order and Transseries Structure of Radiation Reaction
• Introductory Lectures on Resurgence: CERN Summer School 2024
• Noise Effects on Pade Approximants and Conformal Maps
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• BPS Wilson loop in $\mathcal{N}=2$ superconformal $SU(N)$ "orientifold" gauge theory and weak-strong coupling interpolation
• Resurgence, Stokes constants, and arithmetic functions in topological string theory
• Resurgence in the Scalar Quantum Electrodynamics Euler-Heisenberg Lagrangian
• Exponential Asymptotics using Numerical Rational Approximation in Linear Differential Equations
• Uncovering Hidden Patterns: Approximate Resurgent Resummation from Truncated Series
• Pair Production in Real Proper Time and Unitarity Without Borel Ambiguity
• From Divergent Series to Geometry: Resurgence of the Quantum Metric