{
  "annotation_id": "ff4412af-dd60-4087-91b4-f6f27b14e1af",
  "date_created": "2026-03-02T18:02:13.221000Z",
  "date_modified": "2026-03-02T18:02:13.221000Z",
  "file_hash": "0262afcec8bfa431af92d6152142476bd9f93a97a52a11318d61a91834a84b51",
  "private": false,
  "record": {
    "abstract": "In this paper we construct a non-commutative version of the Hopf bundle by\nmaking use of Jaynes-Commings model and so-called Quantum Diagonalization\nMethod. The bundle has a kind of Dirac strings. However, they appear in only\nstates containing the ground one (${\\cal F}\\times \\{\\ket{0}\\} \\cup\n\\{\\ket{0}\\}\\times {\\cal F} \\subset {\\cal F}\\times {\\cal F}$) and don\u0027t appear\nin remaining excited states. This means that classical singularities are not\nuniversal in the process of non-commutativization.\n  Based on this construction we moreover give a non-commutative version of both\nthe Veronese mapping which is the mapping from $\\fukuso P^{1}$ to $\\fukuso\nP^{n}$ with mapping degree $n$ and the spin representation of the group SU(2).\n  We also present some challenging problems concerning how classical\n(beautiful) properties can be extended to the non-commutative case.",
    "arxiv_id": "quant-ph/0502174",
    "authors": [
      "Kazuyuki Fujii"
    ],
    "categories": [
      "quant-ph",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "title": "From Quantum Optics to Non-Commutative Geometry : A Non-Commutative   Version of the Hopf Bundle, Veronese Mapping and Spin Representation",
    "url": "https://arxiv.org/abs/quant-ph/0502174"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b19b8f1a-3bcd-4a65-859d-73b2b1f13bc6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}