{
  "annotation_id": "e48ada15-0886-4272-b82a-a77d70a47dd9",
  "date_created": "2026-03-02T18:01:42.261000Z",
  "date_modified": "2026-03-02T18:01:42.261000Z",
  "file_hash": "e7dd09c1451789f4de7fed38ff6b6db271f289e0ed194c7e134686341a5b79fc",
  "private": false,
  "record": {
    "abstract": "We start to develop the quantization formalism in a hyperbolic Hilbert space.\nGeneralizing Born\u0027s probability interpretation, we found that unitary\ntransformations in such a Hilbert space represent a new class of\ntransformations of probabilities which describe a kind of {\\it hyperbolic\ninterference}. The most interesting problem which was generated by our\ninvestigation is to find experimental evidence of hyperbolic interference. The\nhyperbolic quantum formalism can also be interesting as a new theory of\nprobabilistic waves that can be developed parallely to the standard quantum\ntheory. Comparative analysis of these two wave theories could be useful for\nunderstanding of the role of various structures of the standard quantum\nformalism. In particular, one of distinguishing feature of the hyperbolic\nquantum formalism is the restricted validity of the superposition principle.",
    "arxiv_id": "quant-ph/0101002",
    "authors": [
      "Andrei Khrennikov"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Hyperbolic quantum mechanics",
    "url": "https://arxiv.org/abs/quant-ph/0101002"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f70bea66-3a37-49b0-8607-cd611d65f173",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}