An introduction to resurgence, trans-series and alien calculus
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Publication:2335983
DOI10.1016/J.AOP.2019.167914zbMATH Open1425.81003arXiv1411.3585OpenAlexW1550848762WikidataQ114953137 ScholiaQ114953137MaRDI QIDQ2335983
Author name not available (Why is that?)
Publication date: 18 November 2019
Published in: (Search for Journal in Brave)
Abstract: In these notes we give an overview of different topics in resurgence theory from a physics point of view, but with particular mathematical flavour. After a short review of the standard Borel method for the resummation of asymptotic series, we introduce the class of simple resurgent functions, explaining their importance in physical problems. We define the Stokes automorphism and the alien derivative and discuss these objects in concrete examples using the notion of trans-series expansion. With all the tools introduced, we see how resurgence and alien calculus allow us to extract non-perturbative physics from perturbation theory. To conclude, we apply Morse theory to a toy model path integral to understand why physical observables should be resurgent functions.
Full work available at URL: https://arxiv.org/abs/1411.3585
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