{
  "abstract": "We investigate a planar Dirac oscillator coupled to a spatially uniform \\(\\utwo=\\uone\\times\\su\\) Yang--Mills background. The gauge configuration, adapted from the Dossa--Avossevou construction, contains an Abelian magnetic field \\(B\\), a non-Abelian spatial amplitude \\(β\\), and a non-Abelian scalar amplitude \\(ρ\\). Within the Pauli-reduced formulation, the non-Abelian field strength produces a constant operator on \\(\\mathbb{C}^{2}_{\\mathrm{spin}}\\otimes\\mathbb{C}^{2}_{\\mathrm{iso}}\\). This operator contains a diagonal internal-Zeeman contribution proportional to \\(σ^{3}T^{3}\\) and an off-diagonal spin--isospin term proportional to \\(σ^{1}T^{1}+σ^{2}T^{2}\\). Its diagonalization gives a doubly degenerate aligned branch and two mixed branches with eigenvalues \\[ λ_{\\mathrm{FM}}=\\frac{g^{2}β^{2}}{4m},\\qquad λ_{S}=-\\frac{g^{2}β(β-2ρ)}{4m},\\qquad λ_{T}=-\\frac{g^{2}β(β+2ρ)}{4m}. \\] Consequently, the aligned internal-Zeeman scale is quadratic in \\(β\\), whereas the singlet--triplet separation is linear in \\(βρ\\). The revised formulation makes the sign conventions explicit, verifies the main limiting cases, distinguishes the Pauli-reduced spectrum from a full first-order Dirac diagonalization, and clarifies the physical meaning of the numerical illustrations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.30403",
  "author_total": 1,
  "authors": [
    {
      "name": "Abdelmalek Boumali"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5znvrtzyy8jnd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.30403",
  "fulltext_url": null,
  "id": "5znvrtzyy8jnd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.30403",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Quantum Chromodynamics and Particle Interactions"
    ]
  ],
  "openalex": "W7163078104",
  "pdf_url": "https://arxiv.org/pdf/2605.30403",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5znvrtzyy8jnd.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:04Z",
      "native_id": "2605.30403",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.30403"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Non-Abelian Dirac oscillator in a uniform Yang--Mills background: spin--isospin mixing and singlet--triplet splitting",
  "title_text": "Non-Abelian Dirac oscillator in a uniform Yang--Mills background: spin--isospin mixing and singlet--triplet splitting",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:17Z",
  "url": "https://research.draconitic.com/paper/5znvrtzyy8jnd",
  "venue": "arXiv",
  "versions": []
}