{
  "annotation_id": "7855570e-511c-411d-a42e-46b7453edf2a",
  "date_created": "2026-03-02T18:01:59.598000Z",
  "date_modified": "2026-03-02T18:01:59.598000Z",
  "file_hash": "27f08e2c734768d13f0936d42aed5756fbfae95b1cdf448ced6446c1393639a8",
  "private": false,
  "record": {
    "abstract": "The classical mechanics of a finite number of degrees of freedom requires a\nsymplectic structure on phase space C, but it is independent of any complex\nstructure. On the contrary, the quantum theory is intimately linked with the\nchoice of a complex structure on C. When the latter is a complex-analytic\nmanifold admitting just one complex structure, there is a unique quantisation\nwhose classical limit is C. Then the notion of coherence is the same for all\nobservers. However, when C admits two or more nonbiholomorphic complex\nstructures, there is one different quantisation per different complex structure\non C. The lack of analyticity in transforming between nonbiholomorphic complex\nstructures can be interpreted as the loss of quantum-mechanical coherence under\nthe corresponding transformation. Observers using one complex structure\nperceive as coherent the states that other observers, using a different complex\nstructure, do not perceive as such. This is the notion of a quantum-mechanical\nduality transformation: the relativity of the notion of a quantum.",
    "arxiv_id": "quant-ph/0304143",
    "authors": [
      "J. M. Isidro"
    ],
    "categories": [
      "quant-ph",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1142/S0217732303011873",
    "journal_ref": "Mod.Phys.Lett. A18 (2003) 1975-1990",
    "title": "Duality, Quantum Mechanics and (Almost) Complex Manifolds",
    "url": "https://arxiv.org/abs/quant-ph/0304143"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "166b19d8-e321-468d-b766-ee5d7559c733",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}