{
  "annotation_id": "37415d2e-4b4c-4002-95ff-36907886707c",
  "date_created": "2026-03-02T18:02:41.734000Z",
  "date_modified": "2026-03-02T18:02:41.734000Z",
  "file_hash": "26b8985c07056790480d71cbc160e23ecae43992081b7d944f555f8fe28058b2",
  "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. Its 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  The present first part of this investigation is devoted to the introduction\nof basic concepts on which the fibre bundle approach to quantum mechanics\nrests. We show that the evolution of pure quantum-mechanical states can be\ndescribed as a suitable linear transport along paths, called evolution\ntransport, of the state sections in the Hilbert fibre bundle of states of a\nconsidered quantum system.",
    "arxiv_id": "quant-ph/9803084",
    "authors": [
      "Bozhidar Z. Iliev"
    ],
    "categories": [
      "quant-ph",
      "gr-qc",
      "hep-th",
      "math.DG",
      "math.GT"
    ],
    "doi": "10.1088/0305-4470/34/23/308",
    "journal_ref": "J.Phys.A34:4887-4918,2001",
    "title": "Fibre bundle formulation of nonrelativistic quantum mechanics: I.   Introduction. The evolution transport",
    "url": "https://arxiv.org/abs/quant-ph/9803084"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "aa2f438e-62e2-44ca-971d-2b782502338f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}