Polymer quantum mechanics on compact configuration spaces

[2606.06019] Polymer quantum mechanics on compact configuration spaces Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2606.06019 (quant-ph) [Submitted on 4 Jun 2026 ( v1 ), last revised 15 Aug 2026 (this version, v3)] Title: Polymer quantum mechanics on compact configuration spaces Authors: Maxwell R. Siebersma , Basie Seibert , Samuel Shuman , David A. Craig View a PDF of the paper titled Polymer quantum mechanics on compact configuration spaces, by Maxwell R. Siebersma and 3 other authors View PDF HTML (experimental) Abstract: "Polymer quantum mechanics" is the name given to a quantization scheme inspired by loop quantum gravity in which the configuration space of the theory is chosen to have a discrete topology. Polymer quantization yields a representation of the canonical commutation relations that is genuinely distinct from the conventional "Schrödinger" representation. In this paper, we summarize the main features of polymer quantum mechanics and investigate in detail the polymer quantization of systems with configuration spaces that are classically compact. We show explicitly how using the standard construction of polymer states leads to a Hilbert space of states defined on a finite graph of points. By way of example, we find the exact energy eigenvalues and eigenfunctions for a particle on a ring and a particle in a box defined on such lattices, and discuss similarities and differences from standard Schrödinger quantum mechanics. We also explore the continuum limit of states in these systems, and demonstrate in detail how the exact eigenfunctions in the position representation approach their continuum counterparts. Comments: 43 pages, 8 figures. v2: Minor edits. References added. v3: Minor edits. Typos corrected, references updated. Version that appears in Universe (more or less) Subjects: Quantum Physics (quant-ph) ; General Relativity and Quantum Cosmology (gr-qc) Cite as: arXiv:2606.06019 [quant-ph] (or arXiv:2606.06019v3 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.06019 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Universe 12(8) 246 (2026) Related DOI : https://doi.org/10.3390/universe12080246 Focus to learn more DOI(s) linking to related resources Submission history From: David A. Craig [ view email ] [v1] Thu, 4 Jun 2026 11:09:41 UTC (1,016 KB) [v2] Wed, 24 Jun 2026 10:29:44 UTC (1,023 KB) [v3] Sat, 15 Aug 2026 09:37:33 UTC (1,016 KB) Full-text links: Access Paper: View a PDF of the paper titled Polymer quantum mechanics on compact configuration spaces, by Maxwell R. Siebersma and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-06 Change to browse by: gr-qc 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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