Introduction to Resurgence, Trans-Series and Non-Perturbative Physics II by Gerald Dunne

Explore advanced concepts in quantum field theory and non-perturbative physics in this comprehensive lecture. Delve into topics such as instability and divergence of perturbation theory, Borel summation, resurgent trans-series, and the Euler-Heisenberg effective action. Examine the IR renormalon puzzle in asymptotically free QFT and investigate topological molecules in spatially compactified theories. Learn about analytic continuation of path integrals, the Darboux theorem, and resurgence in quantum mechanics. Discover connections between perturbative and non-perturbative sectors, and explore applications of resurgence in supersymmetric quantum mechanics. Gain insights into cutting-edge research in theoretical physics from expert Gerald Dunne at the International Centre for Theoretical Sciences.

Instability and Divergence of Perturbation Theory
Borel summation in practice
recall: divergence of perturbation theory in QM
Bogomolny/Zinn-Justin mechanism in QM
Borel summation in practice 9 ~ [mg"
Decoding a Resurgent Trans-series
Towards Resurgence in QFT
Dyson's argument QED
Euler-Heisenberg Effective Action 1935
Euler-Heisenberg Effective Action and Schwinger Effect
Euler-Heisenberg and Matrix Models, Large N, Strings, ...
de Sitter/ anti de Sitter effective actions Das & CD, hep-th/0607165
IR Renormalon Puzzle in Asymptotically Free QFT
Topological Molecules in Spatially Compactified Theories CPN-1: regulate scale modulus problem with spatial compactification:
Perturbative Analysis
Non-perturbative Physics Without Instantons
The Bigger Picture:
Towards Analytic Continuation of Path Integrals
All-Orders Steepest Descents: Darboux Theorem
Resurgence in Path Integrals: "Functional Darboux Theorem"
Resurgence in Quantum Mechanics
Uniform WKB & Resurgent Trans-Series Du= ~e-2/1+...+etizv V2x_ T-v 2-1- e+2/4 1+ ...
Connecting Perturbative and Non-Perturbative Sector this proves the Zinn-Justin/Jentschura conjecture:
Resurgence at work
Deconstructing Zero: P/NP Resurgence for SUSY QM
Connecting Perturbative and Non-Perturbative Sector