{
  "abstract": "We study even non-unital Dirac data on the two-dimensional Moyal plane with fixed deformation parameter \\(\\vartheta\\neq0\\), whose Dirac operator is affine in the left and right regular coordinate multipliers, with coefficient matrices \\(T_L\\) and \\(T_R\\). Two invariants organize this class. The right block controls algebra--Dirac transversality: local compactness holds if and only if \\(\\det T_R\\neq0\\), with \\(|\\det T_R|\\) determining the local volume coefficient and \\(\\operatorname{sgn}\\det T_R\\) the oriented Gaussian \\(K\\)-homology pairing. Independently, \\(Γ=\\vartheta(\\det T_L-\\det T_R)\\) controls the spectral regime and, together with \\(|\\det T_R|\\), the exact localized heat trace: \\(Γ\\neq0\\) gives infinitely degenerate Landau levels, while for \\(Γ=0\\) in the transverse regime the spectrum is \\(\\mathbb R\\) with empty point spectrum. Applied to Wallet's Landau--Moyal family, the criterion shows that local compactness survives at the metric-degenerate point \\(ξ_{\\mathrm W}=1\\) but fails at \\(ξ_{\\mathrm W}=-1\\), thereby resolving the local-compactness behaviour at both exceptional one-sided points. We then derive a distinguished affine family from a fixed nondegenerate sector \\((\\hbar_0,\\vartheta_0,B_0)\\) of the kinematical symmetry group of two-dimensional noncommutative quantum mechanics. The sector fixes the effective Moyal scale \\(\\vartheta_{\\mathrm{eff}}=\\vartheta_0/(1-\\vartheta_0B_0/\\hbar_0)\\) and \\(T_R\\), while an affine \\(U(1)_\\star\\) background coupling deforms only the left affine part of the Dirac operator. Consequently, local compactness, noncommutative volume and \\(K\\)-homology class remain unchanged, whereas \\(Γ=\\tfrac12(1-eF_{xy}/B_0)\\) drives a transition at \\(eF_{xy}=B_0\\) from Landau levels to spectrum \\(\\mathbb R\\) with empty point spectrum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.10250",
  "author_total": 3,
  "authors": [
    {
      "name": "Tanmoy Kumar Sarkar"
    },
    {
      "name": "Md. Rafsanjany Jim"
    },
    {
      "name": "S. Hasibul Hassan Chowdhury"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f774whyn911sm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.10250",
  "fulltext_url": null,
  "id": "f774whyn911sm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.10250",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7160965417",
  "pdf_url": "https://arxiv.org/pdf/2605.10250",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f774whyn911sm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2605.10250",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.10250"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Affine Left--Right Dirac Data on the Moyal Plane, with an Application to $U(1)_\\star$ Gauge Coupling in Noncommutative Quantum Mechanics",
  "title_text": "Affine Left--Right Dirac Data on the Moyal Plane, with an Application to U(1)_⋆ Gauge Coupling in Noncommutative Quantum Mechanics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/f774whyn911sm",
  "venue": "arXiv",
  "versions": []
}