{
  "abstract": "We study the one-dimensional linear-potential system as an affine extension of the conformal triangle formed by the free particle, harmonic oscillator (HO) and inverted harmonic oscillator (IHO). Unlike these homogeneous quadratic Hamiltonians in the $sl(2,\\mathbb R)$ sector, the linear-potential Hamiltonian involves the Heisenberg ideal of the Schrödinger algebra. Its direct relation to the free particle is a regular accelerated-frame transformation, developed here at the levels of the classical action, canonical transformation, wave-function intertwiner and propagator; its HO and IHO realizations instead arise through singular displaced-oscillator limits. The Airy energy eigenstates follow from a cubic-phase transform of free-particle momentum eigenstates, from condensation of highly excited harmonic-oscillator levels, and from the limit of a subdominant parabolic-cylinder scattering branch of the inverted oscillator. We also develop a planar extension in homogeneous crossed electric and magnetic fields, where uniform acceleration generates the electric interaction, while uniform rotation produces the Landau coupling and the centrifugal inverted-oscillator term; the guiding-center dynamics yields the Hall drift.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: JHEP 10 (2026) 264",
  "arxiv": "2607.20711",
  "author_total": 2,
  "authors": [
    {
      "name": "Andrey Alcala"
    },
    {
      "name": "Mikhail S. Plyushchay"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4gq6c1c0vhbcd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.20711",
  "fulltext_url": null,
  "id": "4gq6c1c0vhbcd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.20711",
  "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"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Non-Hermitian Physics"
    ]
  ],
  "openalex": "W7170703701",
  "pdf_url": "https://arxiv.org/pdf/2607.20711",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4gq6c1c0vhbcd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2607.20711",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.20711"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Affine Extension of the Free-Particle--Oscillator--Inverted-Oscillator Triangle",
  "title_text": "Affine Extension of the Free-Particle--Oscillator--Inverted-Oscillator Triangle",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/4gq6c1c0vhbcd",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/jhep10(2026)264",
      "pid": "4vg2a6a2cw7s3",
      "relation": "published-as",
      "title": "Affine extension of the free-particle-oscillator-inverted-oscillator triangle",
      "venue": "Journal of High Energy Physics"
    }
  ]
}