Dynamical symmetries of the anisotropic oscillator

[2304.14306] Dynamical symmetries of the anisotropic oscillator Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematical Physics arXiv:2304.14306 (math-ph) [Submitted on 27 Apr 2023 ( v1 ), last revised 27 Jan 2026 (this version, v2)] Title: Dynamical symmetries of the anisotropic oscillator Authors: Akash Sinha , Aritra Ghosh , Bijan Bagchi View a PDF of the paper titled Dynamical symmetries of the anisotropic oscillator, by Akash Sinha and 2 other authors View PDF HTML (experimental) Abstract: It is well known that the Hamiltonian of an $n$-dimensional isotropic oscillator admits an $SU(n)$ symmetry, making the system maximally superintegrable. However, the dynamical symmetries of the anisotropic oscillator are much more subtle. We introduce a novel set of canonical transformations that map an $n$-dimensional anisotropic oscillator to the corresponding isotropic problem. Consequently, the anisotropic oscillator is found to possess the same number of conserved quantities as the isotropic oscillator, making it maximally superintegrable too (commensurate case). The first integrals are explicitly calculated in the case of a two-dimensional anisotropic oscillator and remarkably, they admit closed-form expressions. Comments: v1: Preliminary version, comments are welcome; v2: Includes post-publication corrections of typos and minor errors, as well as clarifying remarks in the Appendix Subjects: Mathematical Physics (math-ph) ; High Energy Physics - Theory (hep-th); Classical Physics (physics.class-ph); Quantum Physics (quant-ph) Cite as: arXiv:2304.14306 [math-ph] (or arXiv:2304.14306v2 [math-ph] for this version) https://doi.org/10.48550/arXiv.2304.14306 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Scr. 98, 095253 (2023) [Corrigendum: Phys. Scr. 101, 149501 (2026)] Related DOI : https://doi.org/10.1088/1402-4896/acf00d Focus to learn more DOI(s) linking to related resources Submission history From: Aritra Ghosh [ view email ] [v1] Thu, 27 Apr 2023 16:21:49 UTC (10 KB) [v2] Tue, 27 Jan 2026 18:47:05 UTC (11 KB) Full-text links: Access Paper: View a PDF of the paper titled Dynamical symmetries of the anisotropic oscillator, by Akash Sinha and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math-ph < prev | next > new | recent | 2023-04 Change to browse by: hep-th math math.MP physics physics.class-ph quant-ph References & Citations INSPIRE HEP NASA ADS Google 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? ) 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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