Resurgence Theory and Holomorphic Quantum Mechanics
Summarize this article with:
Quantum Physics arXiv:2603.26808 (quant-ph) [Submitted on 26 Mar 2026] Title:Resurgence Theory and Holomorphic Quantum Mechanics Authors:M. W. AlMasri View a PDF of the paper titled Resurgence Theory and Holomorphic Quantum Mechanics, by M. W. AlMasri View PDF HTML (experimental) Abstract:In this work, we study the resurgence program in holomorphic quantum mechanics. As a specific problem, we investigate the resurgence in the quartic anharmonic oscillator within holomorphic quantum mechanics, using the Bargmann representation of bosonic operators. In this framework, the perturbative energy series is shown to be Gevrey-1 and Borel summable only after continuation across the Stokes line. The instanton operator, realized as a coherent-state displacement in the Segal--Bargmann space, provides an explicit operatorial bridge between perturbative coefficients and non-perturbative sectors. Alien derivative relations generate the full resurgence triangle characteristic of the Bender--Wu model, and the resummed energy is expressed as a trans-series via a ratio of expectation values involving this instanton operator. As a concrete demonstration, we compute the first seven energy levels ($n=0,\dots,6$) up to sixth order in the coupling $g$; the resulting exact rational coefficients reproduce the classic Bender--Wu results, confirming the consistency and power of the holomorphic resurgence approach. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2603.26808 [quant-ph] (or arXiv:2603.26808v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.26808 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mohammad Walid AlMasri [view email] [v1] Thu, 26 Mar 2026 12:54:07 UTC (16 KB) Full-text links: Access Paper: View a PDF of the paper titled Resurgence Theory and Holomorphic Quantum Mechanics, by M. W. AlMasriView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: hep-th References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)