{
  "annotation_id": "df6a3865-10dc-41b4-b727-8c543d206932",
  "date_created": "2026-03-02T18:02:27.239000Z",
  "date_modified": "2026-03-02T18:02:27.239000Z",
  "file_hash": "b9e21ed06f78df599b1ac6df6645cebdf0436ff48ea0e37e0e8270014f8b3f44",
  "private": false,
  "record": {
    "abstract": "Positive matrices in SL(2,C) have a double physical interpretation; they can\nbe either considered as \"fuzzy projections\" of a spin 1/2 quantum system, or as\nLorentz boosts. In the present paper, concentrating on this second\ninterpretation, we follow the clues given by Pertti Lounesto and, using the\nclassical Clifford algebraic methods, interpret them as conformal maps of the\n\"heavenly sphere\" S^2. The fuzziness parameter of the first interpretation\nbecomes the \"boost velocity\" in the second one. We discuss simple iterative\nfunction systems of such maps, and show that they lead to self--similar fractal\npatterns on S^2. The final section of this paper is devoted to an informal\ndiscussion of the relations between these concepts and the problems in the\nfoundations of quantum theory, where the interplay between different kinds of\nalgebras and maps may enable us to describe not only the continuous evolution\nof wave functions, but also quantum jumps and \"events\" that accompany these\njumps. Paper dedicated to the memory of Pertti Lounesto.",
    "arxiv_id": "quant-ph/0604023",
    "authors": [
      "Arkadiusz Jadczyk"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum Fractals. Geometric modeling of quantum jumps with conformal   maps",
    "url": "https://arxiv.org/abs/quant-ph/0604023"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0a19725b-9bb9-4cd3-a0cb-e407507e6a35",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}