{
  "abstract": "We review and develop the many-body spectral theory of ideal anyons, i.e. identical quantum particles in the plane whose exchange rules are governed by unitary representations of the braid group on N strands. Allowing for arbitrary rank (dependent on N ) and non-abelian representations, and letting $$N \\rightarrow \\infty $$ N → ∞ , this defines the ideal non-abelian many-anyon gas. We compute exchange operators and phases for a common and wide class of representations defined by fusion algebras, including the Fibonacci and Ising anyon models. Furthermore, we extend methods of statistical repulsion (Poincaré and Hardy inequalities) and a local exclusion principle (also implying a Lieb–Thirring inequality) developed for abelian anyons to arbitrary geometric anyon models, i.e. arbitrary sequences of unitary representations of the braid group, for which two-anyon exchange is nontrivial.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Uppsala University, Box 524, SE-751 20, Uppsala, Sweden",
    "Stockholm Mathematics Centre (SMC), Stockholm, Sweden"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Douglas Lundholm",
      "orcid": "0000-0003-3456-5846"
    },
    {
      "affs": [
        1
      ],
      "name": "Viktor Qvarfordt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0htsphzqdk3rg.bib",
  "cited_by": 16,
  "doi": "10.1007/s11785-026-02050-z",
  "fulltext_url": null,
  "id": "0htsphzqdk3rg",
  "issns": [
    "1661-8254",
    "1661-8262"
  ],
  "landing_url": "https://doi.org/10.1007/s11785-026-02050-z",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W3087773967",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s11785-026-02050-z.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": "Birkhäuser",
  "ris": "https://research.draconitic.com/paper/0htsphzqdk3rg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "W3087773967",
      "source": "openalex",
      "url": "https://doi.org/10.1007/s11785-026-02050-z"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Spectral Theory in Mathematical Physics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Exchange and Exclusion in the Non-abelian Anyon Gas",
  "title_text": "Exchange and Exclusion in the Non-abelian Anyon Gas",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T13:20:36Z",
  "url": "https://research.draconitic.com/paper/0htsphzqdk3rg",
  "venue": "Complex Analysis and Operator Theory",
  "versions": []
}