{
  "annotation_id": "40bfcf84-2e3f-484a-aac1-612209eb81d5",
  "date_created": "2026-03-02T18:02:37.271000Z",
  "date_modified": "2026-03-02T18:02:37.271000Z",
  "file_hash": "508feddba7575da5bb08cf3162e9060fa59c32fa1bf1bca21002155a5d9e9256",
  "private": false,
  "record": {
    "abstract": "Thought experiments about the physical nature of set theoretical\ncounterexamples to the axiom of choice motivate the investigation of peculiar\nconstructions, e.g. an infinite dimensional Hilbert space with a modular\nquantum logic. Applying a concept due to BENIOFF, we identify the intrinsically\neffective Hamiltonians with those observables of quantum theory which may\ncoexist with a failure of the axiom of choice. Here a self adjoint operator is\nintrinsically effective, iff the Schroedinger equation of its generated\nsemigroup is soluble by means of eigenfunction series expansions.",
    "arxiv_id": "quant-ph/9501018",
    "authors": [
      "N. Brunner",
      "K. Svozil",
      "M. Baaz"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/BF02849839",
    "journal_ref": "NuovoCim.B110:1397-1414,1995",
    "title": "Effective Quantum Observables",
    "url": "https://arxiv.org/abs/quant-ph/9501018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7a966e5f-c7ba-4a23-a8a6-1a0054b9a0e5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}