{
  "annotation_id": "90b87e5b-9bf7-404b-b729-3783ffc7b451",
  "date_created": "2026-03-02T18:01:59.468000Z",
  "date_modified": "2026-03-02T18:01:59.468000Z",
  "file_hash": "a45a659b252272cd0943b99c577e60cf8e2e0ccd3ead8768495a802d6dc02be4",
  "private": false,
  "record": {
    "abstract": "We investigate consequences of allowing the Hilbert space of a quantum system\nto have a time-dependent metric. For a given possibly nonstationary quantum\nsystem, we show that the requirement of having a unitary Schreodinger\ntime-evolution identifies the metric with a positive-definite (Ermakov-Lewis)\ndynamical invariant of the system. Therefore the geometric phases are\ndetermined by the metric. We construct a unitary map relating a given\ntime-independent Hilbert space to the time-dependent Hilbert space defined by a\npositive-definite dynamical invariant. This map defines a transformation that\nchanges the metric of the Hilbert space but leaves the Hamiltonian of the\nsystem invariant. We propose to identify this phenomenon with a quantum\nmechanical analogue of the principle of general covariance of General\nRelativity. We comment on the implications of this principle for geometrically\nequivalent quantum systems and investigate the underlying symmetry group.",
    "arxiv_id": "quant-ph/0306200",
    "authors": [
      "Ali Mostafazadeh"
    ],
    "categories": [
      "quant-ph",
      "gr-qc",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1016/j.physleta.2003.12.008",
    "journal_ref": "Phys.Lett. A320 (2004) 375-382",
    "title": "Time-Dependent Hilbert Spaces, Geometric Phases, and General Covariance   in Quantum Mechanics",
    "url": "https://arxiv.org/abs/quant-ph/0306200"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "74fb28b1-ebec-4632-9c2e-5ad37eba8abb",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}