{
  "annotation_id": "c348fb5d-c1ff-42ba-b443-6fd8722adc4d",
  "date_created": "2026-03-02T18:02:17.266000Z",
  "date_modified": "2026-03-02T18:02:17.266000Z",
  "file_hash": "e52d9cb352b077c2618d9c1a751fa0e2951bef717431b6ca7828085d3afbd5a5",
  "private": false,
  "record": {
    "abstract": "We provide an answer to the long standing problem of mixing quantum and\nclassical dynamics within a single formalism. The construction is based on\np-mechanical derivation (quant-ph/0212101, quant-ph/0304023) of quantum and\nclassical dynamics from the representation theory of the Heisenberg group. To\nachieve a quantum-classical mixing we take the product of two copies of the\nHeisenberg group which represent two different Planck\u0027s constants. In\ncomparison with earlier guesses our answer contains an extra term of analytical\nnature, which was not obtained before in purely algebraic setup.\n  Keywords: Moyal brackets, Poisson brackets, commutator, Heisenberg group,\norbit method, representation theory, Planck\u0027s constant, quantum-classical\nmixing",
    "arxiv_id": "quant-ph/0506122",
    "authors": [
      "Vladimir V. Kisil"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1209/epl/i2005-10324-7",
    "journal_ref": "Europhys. Lett., 72 (6), pp. 873-?879 (2005)",
    "title": "A Quantum-Classical Brackets from p-Mechanics",
    "url": "https://arxiv.org/abs/quant-ph/0506122"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "aa38b25b-b3a8-400d-9500-396b013d3158",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}