{
  "abstract": "For the 1D generalized Coulomb problems--a family that includes the quantizations of the 1D generalized Kepler problems of Ma-Meng-Xiao \\cite{MMX2025}--we construct two explicit unitary intertwiners $\\hatι_{\\pm}$, the quantum analogs of the classical symmetry regularization maps $ι_{\\pm}$ of \\cite{MMX2025}, that unitarily identify each $H_κ$-energy-definite portion of the Hilbert space $L^{2}(\\mathbb{R}_{>0},\\mathrm{d}q)$ with a unitary lowest-weight representation of $\\widetilde{\\mathrm{SL}}(2,\\mathbb{R})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.08900",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhanqiang Bai"
    },
    {
      "name": "Junwei Ma"
    },
    {
      "name": "Guowu Meng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cevmyn03ehd71.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.08900",
  "fulltext_url": null,
  "id": "cevmyn03ehd71",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.08900",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.08900",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cevmyn03ehd71.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2606.08900",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.08900"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Symmetry Regularization of 1D Generalized Coulomb Problems",
  "title_text": "Symmetry Regularization of 1D Generalized Coulomb Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/cevmyn03ehd71",
  "venue": "arXiv",
  "versions": []
}