Introductory Lectures on Resurgence: CERN Summer School 2024
arXiv:2511.15528 · doi:10.1140/epjs/s11734-026-02135-y
Abstract
A set of four introductory lectures on Resurgent Asymptotics for Physics (``resurgence") at the CERN Summer School: Continuum Foundations of Lattice Gauge Theories, July 2024. Lecture 1: The Airy function and the Stokes phenomenon. Lecture 2: The nonlinear Stokes phenomenon. Lecture 3: Resurgence in QFT: the Heisenberg-Euler effective action. Lecture 4: Resurgent continuation and summation. The emphasis of these lectures is on physically motivated examples. The lectures include many exercises designed to illustrate some of the key ideas of resurgence.
65 pages, 13 figures
References in corpus (31)
- Extremely high-intensity laser interactions with fundamental quantum systems
- New Relations for Gauge-Theory Amplitudes
- Perturbative Quantum Field Theory in the String-Inspired Formalism
- The Effective Field Theorist's Approach to Gravitational Dynamics
- Advances in QED with intense background fields
- Worldline Instantons and Pair Production in Inhomogeneous Fields
- Heisenberg-Euler Effective Lagrangians : Basics and Extensions
- Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
- Classical black hole scattering from a worldline quantum field theory
- Worldline Instantons II: The Fluctuation Prefactor
- A Primer on Resurgent Transseries and Their Asymptotics
- Momentum signatures for Schwinger pair production in short laser pulses with a sub-cycle structure
- An Introduction to Resurgence, Trans-Series and Alien Calculus
- Conceptual Design Report for the LUXE Experiment
- The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses
- From Useful Algorithms for Slowly Convergent Series to Physical Predictions Based on Divergent Perturbative Expansions
- Generating Non-perturbative Physics from Perturbation Theory
- New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
- Ramsey Fringes and Time-domain Multiple-Slit Interference from Vacuum
- Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
- Functional Determinants in Quantum Field Theory
- Borel Summation of the Derivative Expansion and Effective Actions
- Physical Resurgent Extrapolation
- Resurgent Extrapolation: Rebuilding a Function from Asymptotic Data. Painleve I
- Uniformization and Constructive Analytic Continuation of Taylor Series
- Conformal and Uniformizing Maps in Borel Analysis
- Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition
- Uniformizing Lee-Yang Singularities
- Resurgence of the Effective Action in Inhomogeneous Fields
- Resurgence of the Tilted Cusp Anomalous Dimension
- Resurgent Trans-Series for Generalized Hastings-McLeod Solutions