{
  "abstract": "We develop a unified algebraic approach to spin-boson transformations based on the formalism of $f$-deformed oscillators. In the single-mode case, we show that the Holstein-Primakoff and Dyson-Maleev transformations, together with the interpolating $α$-family, arise as different factorizations of the same algebraically determined object. The standard spin-boson mappings can thus be interpreted as realizations of a common structure, which makes it possible to clearly separate the exact algebraic content on the physical subspace from effects associated with non-Hermiticity, the choice of metric, and extensions beyond the physical subspace. In the two-mode case, the same approach yields both deformed versions of the Jordan-Schwinger transformation and new exact two-mode realizations. Our results provide a unified description of known spin-boson transformations and naturally lead to new bosonic representations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22502",
  "author_total": 4,
  "authors": [
    {
      "name": "Vladimir A. Orlov"
    },
    {
      "name": "Liubov A. Markovich"
    },
    {
      "name": "Andrey V. Mikheyenkov"
    },
    {
      "name": "Vladimir I. Man'ko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4vz23bmbd2a78.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22502",
  "fulltext_url": null,
  "id": "4vz23bmbd2a78",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22502",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.other"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Non-Hermitian Physics"
    ]
  ],
  "openalex": "W7214049281",
  "pdf_url": "https://arxiv.org/pdf/2609.22502",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4vz23bmbd2a78.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.22502",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22502"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.other",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Spin-Boson Mappings in the Formalism of $f$-Deformations",
  "title_text": "Spin-Boson Mappings in the Formalism of f-Deformations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/4vz23bmbd2a78",
  "venue": "arXiv",
  "versions": []
}