{
  "abstract": "We derive the Runge-Lenz vector of the five-dimensional Kepler problem from the eight-dimensional harmonic oscillator through symplectic reduction. By rewriting the moment maps of the harmonic oscillator in terms of five-dimensional gamma matrices and the $\\mathfrak{su}(2)$ generators associated with the symplectic reduction, we identify the moment map expected to yield the Runge-Lenz vector. We then perform the reduction with respect to the SU(2) symmetry, derive the five-dimensional Kepler Hamiltonian, and show explicitly that the identified moment map reduces to the Runge-Lenz vector.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27750",
  "author_total": 5,
  "authors": [
    {
      "name": "Hitoshi Ikemori"
    },
    {
      "name": "Shinsaku Kitakado"
    },
    {
      "name": "Yoshimitsu Matsui"
    },
    {
      "name": "Toshiyuki Okubo"
    },
    {
      "name": "Toshiro Sato"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7kbrr7g0d6017.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27750",
  "fulltext_url": null,
  "id": "7kbrr7g0d6017",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27750",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
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      "arxiv",
      "math.MP"
    ],
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      "arxiv",
      "physics.class-ph"
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    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "openalex": "W7223145995",
  "pdf_url": "https://arxiv.org/pdf/2610.27750",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7kbrr7g0d6017.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27750",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27750"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "5D Runge-Lenz Vector from Symplectic Reduction of 8D Harmonic Oscillator",
  "title_text": "5D Runge-Lenz Vector from Symplectic Reduction of 8D Harmonic Oscillator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/7kbrr7g0d6017",
  "venue": "arXiv",
  "versions": []
}