{
  "annotation_id": "50bfcc23-7ec5-462e-8d1c-ee62f83397fb",
  "date_created": "2026-03-02T18:02:43.865000Z",
  "date_modified": "2026-03-02T18:02:43.865000Z",
  "file_hash": "4cce1d03eabb36e3fbee03d815a81929720cf1a66f9a7f2c499a38e10472b564",
  "private": false,
  "record": {
    "abstract": "We propose a new systematic fibre bundle formulation of nonrelativistic\nquantum mechanics. The new form of the theory is equivalent to the usual one\nbut it is in harmony with the modern trends in theoretical physics and\npotentially admits new generalizations in different directions. In it a pure\nstate of some quantum system is described by a state section (along paths) of a\n(Hilbert) fibre bundle. It\u0027s evolution is determined through the bundle\n(analogue of the) Schr\\\"odinger equation. Now the dynamical variables and the\ndensity operator are described via bundle morphisms (along paths). The\nmentioned quantities are connected by a number of relations derived in this\nwork.\n  In this third part of our series we investigate the bundle analogues of the\nconventional pictures of motion. In particular, there are found the state\nsections and bundle morphisms corresponding to state vectors and observables\nrespectively. The equations of motion for these quantities are derived too.\nUsing the results obtained, we consider from the bundle view-point problems\nconcerning the integrals of motion. An invariant (bundle) necessary and\nsufficient conditions for a dynamical variable to be an integral of motion are\nfound.",
    "arxiv_id": "quant-ph/9806046",
    "authors": [
      "Bozhidar Z. Iliev"
    ],
    "categories": [
      "quant-ph",
      "gr-qc",
      "hep-th"
    ],
    "doi": "10.1088/0305-4470/34/23/310",
    "journal_ref": "J.Phys.A34:4935-4950,2001",
    "title": "Fibre bundle formulation of nonrelativistic quantum mechanics. III.   Pictures and integrals of motion",
    "url": "https://arxiv.org/abs/quant-ph/9806046"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5095d68c-9332-4132-8e8d-134a09a6d436",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}