Proof of Spin-Statistics Theorem in Quantum Mechanics of Identical Particles
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Quantum Physics arXiv:2512.12071 (quant-ph) [Submitted on 12 Dec 2025] Title:Proof of Spin-Statistics Theorem in Quantum Mechanics of Identical Particles Authors:Takafumi Kita View a PDF of the paper titled Proof of Spin-Statistics Theorem in Quantum Mechanics of Identical Particles, by Takafumi Kita View PDF HTML (experimental) Abstract:A nonrelativistic proof of the spin-statistics theorem is given in terms of the field operators satisfying commutation and anticommutation relations, which are introduced here in the coordinate space as a means to build the permutation symmetry into the brackets of identical particles. An eigenvalue problem of a $\pi$-rotation for a product of two annihilation operators is combined with an analysis on its rotational property to prove the connection that the field operators for integral-spin and half-integral-spin particles obey the commutation and anticommutation relations, respectively. Comments: Subjects: Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Superconductivity (cond-mat.supr-con) Cite as: arXiv:2512.12071 [quant-ph] (or arXiv:2512.12071v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.12071 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Takafumi Kita [view email] [v1] Fri, 12 Dec 2025 22:33:26 UTC (9 KB) Full-text links: Access Paper: View a PDF of the paper titled Proof of Spin-Statistics Theorem in Quantum Mechanics of Identical Particles, by Takafumi KitaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cond-mat cond-mat.quant-gas cond-mat.stat-mech cond-mat.str-el cond-mat.supr-con 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?)