{
  "abstract": "We develop a systematic algebraic approach, based on the Wei--Norman factorization method, to the normal ordering of exponential bosonic operators and apply it to derive analytical excitonic form factors in two-dimensional semiconducting materials. By introducing an auxiliary parameter, the normal-ordering problem is reduced to a system of ordinary differential equations determined by the commutation relations of the underlying closed Lie algebra. The approach is first illustrated for exponential operators associated with the Heisenberg--Weyl and $su(1,1)$ algebras, and is then extended to two-mode bosonic operators involving $su(2)$ and a six-generator closed algebra that contains two coupled $su(1,1)$ subalgebras. For the excitonic application, the Levi--Civita transformation maps the two-dimensional exciton problem onto an oscillator representation, providing a natural formulation in terms of bosonic creation and annihilation operators. Combined with the Laplace and Fourier representations of the Rytova--Keldysh potential, this formulation reduces the interaction matrix elements to the evaluation of exponential bosonic form factors. The isotropic problem is governed by a three-generator $su(1,1)$ algebra, whereas the anisotropic case requires the full six-generator algebra together with an additional $su(2)$ factorization. Explicit analytical expressions for both form factors, $\\langle e^{-rt}\\rangle$ and $\\langle e^{i\\mathbf q\\cdot\\mathbf r}\\rangle$, are obtained, providing useful building blocks for matrix-element calculations in two-dimensional excitonic systems and potentially in other quantum problems involving exponential bosonic operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13884",
  "author_total": 4,
  "authors": [
    {
      "name": "Duy-Anh P. Nguyen"
    },
    {
      "name": "Ngoc-Tram D. Hoang"
    },
    {
      "name": "Dang-Khoa D. Le"
    },
    {
      "name": "Van-Hoang Le"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cw5c083jrd3q1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13884",
  "fulltext_url": null,
  "id": "cw5c083jrd3q1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13884",
  "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",
      "cond-mat.mtrl-sci"
    ],
    [
      "openalex",
      "3107|Semiconductor Quantum Structures and Devices"
    ]
  ],
  "openalex": "W7213249456",
  "pdf_url": "https://arxiv.org/pdf/2609.13884",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cw5c083jrd3q1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.13884",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13884"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "A Direct Algebraic Approach to Normal Ordering of Exponential Bosonic Operators with Applications to Two-Dimensional Excitonic Form Factors",
  "title_text": "A Direct Algebraic Approach to Normal Ordering of Exponential Bosonic Operators with Applications to Two-Dimensional Excitonic Form Factors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/cw5c083jrd3q1",
  "venue": "arXiv",
  "versions": []
}