{
  "annotation_id": "f2b4100b-ee59-4e0a-9ded-23096de6d830",
  "date_created": "2026-03-02T18:02:34.705000Z",
  "date_modified": "2026-03-02T18:02:34.705000Z",
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  "record": {
    "abstract": "Classically the Harmonic Oscillator (HO) is the generic example for the use\nof angle and action variables phi in R mod 2 pi and I \u003e 0. But the symplectic\ntransformation (\\phi,I) to (q,p) is singular for (q,p) = (0,0). Globally\n{(q,p)} has the structure of the plane R^2, but {(phi,I)} that of the punctured\nplane R^2 -(0,0). This implies qualitative differences for the QM of the two\nphase spaces: The quantizing group for the plane R^2 consists of the (centrally\nextended) translations generated by {q,p,1}, but the corresponding group for\n{(phi,I)} is SO(1,2) = Sp(2,R)/Z_2, (Sp(2,R): symplectic group of the plane),\nwith Lie algebra basis {h_0 = I, h_1 = I cos phi, h_2 = - I sin phi}. In the QM\nfor the (phi,I)-model the three h_j correspond to self-adjoint generators K_j,\nj=0,1,2, of irreducible unitary representations (positive discrete series) for\nSO(1,2) or one of its infinitely many covering groups, the Bargmann index k \u003e 0\nof which determines the ground state energy E (k, n=0) = hbar omega k of the\n(phi,I)-Hamiltonian H(K). For an m-fold covering the lowest possible value is\nk=1/m, which can be made arbitrarily small! The operators Q and P, now\nexpressed as functions of the K_j, keep their usual properties, but the richer\nstructure of the K_j quantum model of the HO is ``erased\u0027\u0027 when passing to the\nsimpler Q,P model! The (phi,I)-variant of the HO implies many experimental\ntests: Mulliken-type experiments for isotopic diatomic molecules, experiments\nwith harmonic traps for atoms, ions and BE-condensates, with the (Landau)\nlevels of charged particles in magnetic fields, with the propagation of light\nin vacuum, passing through electric or magnetic fields. Finally it leads to a\nnew theoretical estimate for the quantum vacuum energy of fields and its\nrelation to the cosmological constant.",
    "arxiv_id": "quant-ph/0612032",
    "authors": [
      "H. A. Kastrup"
    ],
    "categories": [
      "quant-ph",
      "astro-ph",
      "hep-th",
      "math-ph",
      "math.MP",
      "physics.atom-ph"
    ],
    "doi": "10.1002/andp.200610245",
    "journal_ref": "AnnalenPhys.16:439-528,2007",
    "title": "A New Look at the Quantum Mechanics of the Harmonic Oscillator",
    "url": "https://arxiv.org/abs/quant-ph/0612032"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5a88233a-8ce7-48e4-bcdf-4a35a49e60f3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}