{
  "annotation_id": "bce47688-0f61-4f46-b35f-49f44e2b6d23",
  "date_created": "2026-03-02T18:02:40.448000Z",
  "date_modified": "2026-03-02T18:02:40.448000Z",
  "file_hash": "353c553c6558804800a97c2c5d324cd6ffd1ec1da5ed064f75e0a1a44661333d",
  "private": false,
  "record": {
    "abstract": "In classical mechanics, the system of two coupled harmonic oscillators is\nshown to possess the symmetry of the Lorentz group O(3,3) applicable to a\nsix-dimensional space consisting of three space-like and three time-like\ncoordinates, or SL(4,r) in the four-dimensional phase space consisting of two\nposition and two momentum variables. In quantum mechanics, the symmetry is\nreduced to that of O(3,2) or Sp(4), which is a subgroup of O(3,3) or SL(4,r)\nrespectively. It is shown that among the six Sp(4)-like subgroups, only one\npossesses the symmetry which can be translated into the group of unitary\ntransformations in quantum mechanics. In quantum mechanics, there is the lower\nbound in the size of phase space for each mode determined by the uncertainty\nprinciple while there are no restriction on the phase-space size in classical\nmechanics. This is the reason why the symmetry is smaller in quantum mechanics.",
    "arxiv_id": "quant-ph/9704005",
    "authors": [
      "D. Han",
      "Y. S. Kim",
      "Marilyn E. Noz"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "title": "O(3,3)-like Symmetries of Coupled Harmonic Oscillators",
    "url": "https://arxiv.org/abs/quant-ph/9704005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a6b66b29-c115-465d-a991-531a39dcb520",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}