{
  "abstract": "The Wheeler-DeWitt equation of a flat Friedmann-Lemaitre-Robertson-Walker universe filled with pressureless dust and a cosmological constant in unimodular gravity reduces, for a specific factor ordering and a specific self-adjoint extension, to the $l=0$ radial Schrödinger equation of a hydrogen atom. We revisit this correspondence from the point of view of the Green's functions and the Duru-Kleinert path integrals. Working directly with the reduced operator on the half-line, we obtain the Green's function in Whittaker form and fix its normalization by a Wronskian argument. Its Gamma-function poles give the reduced-operator spectrum which recovers the quantization of the negative cosmological term. We also perform the operator-level Duru-Kleinert transformation, whose Jacobian generates a barrier which after rescaling is exactly the centrifugal barrier of a two-dimensional oscillator. Retaining it reproduces the Coulomb pole condition. For positive cosmological constant, we give the continuum spectral measure and the Sommerfeld factor.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.18983",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiao-Kan Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7q7z25yca23mz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.18983",
  "fulltext_url": null,
  "id": "7q7z25yca23mz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.18983",
  "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",
      "gr-qc"
    ],
    [
      "openalex",
      "3109|Noncommutative and Quantum Gravity Theories"
    ]
  ],
  "openalex": "W7203886253",
  "pdf_url": "https://arxiv.org/pdf/2608.18983",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7q7z25yca23mz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2608.18983",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.18983"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Duru-Kleinert Path Integral in Unimodular Quantum Cosmology",
  "title_text": "Duru-Kleinert Path Integral in Unimodular Quantum Cosmology",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/7q7z25yca23mz",
  "venue": "arXiv",
  "versions": []
}