{
  "annotation_id": "c9afaad2-a0bf-4b41-adb8-46e340f5dcc4",
  "date_created": "2026-03-02T18:01:56.378000Z",
  "date_modified": "2026-03-02T18:01:56.378000Z",
  "file_hash": "9e1e282a05a20aad46c0628113e661c90047752f44db8d47ce1e21540f48e83e",
  "private": false,
  "record": {
    "abstract": "In this paper, the projective geometry is used to describe the features of\nspherical manifold and discreteness in quantum evolution. As a system evolves\nin time the state vector changes and it traces out a curve in Hilbert space.\nGeometrically, the evolution is represented as a closed curve in the projective\nHilbert space. In recent times many attempts have been made to describe\n\u0027length\u0027, \u0027distance\u0027, and \u0027geometric phases\u0027 and also \u0027parallel transport\u0027and\nsymplectic geometry in various ways in the projective Hilbert space, during\nquantum evolution. It is shown in this paper that for the quantum evolution in\nray space, spherical manifold and features of discreteness can be described\ngeometrically.",
    "arxiv_id": "quant-ph/0301173",
    "authors": [
      "Aalok Pandya",
      "Ashok K. Nagawat"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Spherical Manifold in Quantum Evolution",
    "url": "https://arxiv.org/abs/quant-ph/0301173"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a762c01f-ac5d-4d4e-82c8-4c9db808ad35",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}