{
  "annotation_id": "48a5d00d-abd8-416d-81b9-06454047be67",
  "date_created": "2026-03-02T18:02:38.194000Z",
  "date_modified": "2026-03-02T18:02:38.194000Z",
  "file_hash": "eaf9e9cbf865ea8c9eca66928db1f0cd741262824fc6c195696cde4ef6e82542",
  "private": false,
  "record": {
    "abstract": "text of abstract (We present a utilitarian review of the family of matrix\ngroups $Sp(2n,\\Re)$, in a form suited to various applications both in optics\nand quantum mechanics. We contrast these groups and their geometry with the\nmuch more familiar Euclidean and unitary geometries. Both the properties of\nfinite group elements and of the Lie algebra are studied, and special attention\nis paid to the so-called unitary metaplectic representation of $Sp(2n,\\Re)$.\nGlobal decomposition theorems, interesting subgroups and their generators are\ndescribed. Turning to $n$-mode quantum systems, we define and study their\nvariance matrices in general states, the implications of the Heisenberg\nuncertainty principles, and develop a U(n)-invariant squeezing criterion. The\nparticular properties of Wigner distributions and Gaussian pure state\nwavefunctions under $Sp(2n,\\Re)$ action are delineated.)",
    "arxiv_id": "quant-ph/9509002",
    "authors": [
      "Arvind",
      "B. Dutta",
      "N. Mukunda",
      "R. Simon"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/BF02848172",
    "journal_ref": "Pramana 45 (1995) 471",
    "title": "The Real Symplectic Groups in Quantum Mechanics and Optics",
    "url": "https://arxiv.org/abs/quant-ph/9509002"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "57a6dcec-7fa6-4180-b09b-72c83f9c3c4f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}