{
  "abstract": "We present a novel approach to the superintegrability of collective Hamiltonians invariant under a Hamiltonian action of a connected semisimple compact Lie group, $G$, on a symplectic manifold, $M$. By exploiting a Hamiltonian torus action that goes back to Guillemin and Sternberg [GS,1983], we demonstrate that the functional dimensions of $\\mathfrak{H} := \\mathcal{J}^*(C^\\infty(\\mathfrak{g}^*)^G)$, where $\\mathcal{J}: M \\to \\mathfrak{g}^*$ is the momentum map of the $G$ action, and its centralizer $\\mathfrak{F}$ in $C^\\infty(M)$ satisfy the equality $\\mathrm{ddim}(\\mathfrak{H}) + \\mathrm{ddim}(\\mathfrak{F}) = \\mathrm{dim}(M)$. Together with a non-triviality condition, this ensures that the Abelian Poisson algebra $\\mathfrak{H}\\subset C^\\infty(M)$ represents a superintegrable system, and it also follows that the momentum map of the GS torus action yields action variables for the system. Our work provides a new insight into collective superintegrability complementing earlier results of Bolsinov and Jovanović.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.01878",
  "author_total": 1,
  "authors": [
    {
      "name": "L. Feher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9zt50q5h62p4g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.01878",
  "fulltext_url": null,
  "id": "9zt50q5h62p4g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.01878",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nlin.SI"
    ],
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      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "openalex": "W7172419030",
  "pdf_url": "https://arxiv.org/pdf/2608.01878",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9zt50q5h62p4g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "2608.01878",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.01878"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Collective superintegrable systems from the Guillemin--Sternberg torus action",
  "title_text": "Collective superintegrable systems from the Guillemin--Sternberg torus action",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/9zt50q5h62p4g",
  "venue": "arXiv",
  "versions": []
}