{
  "annotation_id": "4251c4e5-1f0f-4828-b708-07c31b67a216",
  "date_created": "2026-03-02T18:02:40.510000Z",
  "date_modified": "2026-03-02T18:02:40.510000Z",
  "file_hash": "a553309a42193b310a668f4111fe0aed2cbf804b849fd5d43c6873cc38816acb",
  "private": false,
  "record": {
    "abstract": "The relativistic conception of space and time is challenged by the quantum\nnature of physical observables. It has been known for a long time that\nPoincar\\\u0027e symmetry of field theory can be extended to the larger conformal\nsymmetry. We use these symmetries to define quantum observables associated with\npositions in space-time, in the spirit of Einstein theory of relativity. This\nconception of localisation may be applied to massive as well as massless\nfields. Localisation observables are defined as to obey Lorentz covariant\ncommutations relations and in particular include a time observable conjugated\nto energy. Whilst position components do not commute in presence of a\nnon-vanishing spin, they still satisfy quantum relations which generalise the\ndifferential laws of classical relativity. We also give of these observables a\nrepresentation in terms of canonical spatial positions, canonical spin\ncomponents and a proper time operator conjugated to mass. These results plead\nfor a new representation not only of space-time localisation but also of\nmotion.",
    "arxiv_id": "quant-ph/9706036",
    "authors": [
      "Marc-Thierry Jaekel",
      "Serge Reynaud"
    ],
    "categories": [
      "quant-ph",
      "gr-qc"
    ],
    "doi": "10.1023/A:1018716111971",
    "journal_ref": "Found.Phys. 28 (1998) 439-456",
    "title": "Conformal Symmetry and Quantum Relativity",
    "url": "https://arxiv.org/abs/quant-ph/9706036"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "30d78421-5285-4862-bfb4-b8adbb7936ad",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}