{
  "annotation_id": "405a85e6-98d9-4111-a546-d34ea457b12c",
  "date_created": "2026-03-02T18:02:34.427000Z",
  "date_modified": "2026-03-02T18:02:34.427000Z",
  "file_hash": "12ca6dc328ac23f0015619b991ce0841c0b028f6d85f27eaaac9fd2f05afe795",
  "private": false,
  "record": {
    "abstract": "This paper presents a comprehensive perspective of the metric of quantum\nstates with a focus on the background independent metric structures. We also\nexplore the possibilities of geometrical formulations of quantum mechanics\nbeyond the quantum state space and Kahler manifold. The metric of quantum\nstates in the classical configuration space with the pseudo-Riemannian\nsignature and its possible applications are explored. On contrary to the common\nperception that a metric for quantum state can yield a natural metric in the\nconfiguration space with the limit when Planck constant vanishes, we obtain the\nmetric of quantum states in the configuration space without imposing this\nlimiting condition. Here, Planck constant is absorbed in the quantity like Bohr\nradii. While exploring the metric structure associated with Hydrogen like atom,\nwe witness another interesting finding that the invariant lengths appear in the\nmultiple of Bohr radii.",
    "arxiv_id": "quant-ph/0701189",
    "authors": [
      "Aalok"
    ],
    "categories": [
      "quant-ph",
      "gr-qc",
      "hep-th"
    ],
    "doi": "10.1007/s10773-007-9438-7",
    "journal_ref": "Int. J. Theor. Phys. 46 (2007) 3216-3229",
    "title": "Background Independent Quantum Mechanics, Metric of Quantum States, and   Gravity: A Comprehensive Perspective",
    "url": "https://arxiv.org/abs/quant-ph/0701189"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "33905602-0b66-4101-be7d-b5384ccd718a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}