{
  "annotation_id": "09c408a3-9fe3-41dc-9055-38fb148b21fc",
  "date_created": "2026-03-02T18:01:56.555000Z",
  "date_modified": "2026-03-02T18:01:56.555000Z",
  "file_hash": "1643bb687b7873ad2a85337f7f881ac391956cec505d63d171becfa3a741745e",
  "private": false,
  "record": {
    "abstract": "Observables of quantum or classical mechanics form algebras called quantum or\nclassical Hamilton algebras respectively (Grgin E and Petersen A (1974) {\\it J\nMath Phys} {\\bf 15} 764\\cite{grginpetersen}, Sahoo D (1977) {\\it Pramana} {\\bf\n8} 545\\cite{sahoo}). We show that the tensor-product of two quantum Hamilton\nalgebras, each characterized by a different Planck\u0027s constant is an algebra of\nthe same type characterized by yet another Planck\u0027s constant. The algebraic\nstructure of mixed quantum and classical systems is then analyzed by taking the\nlimit of vanishing Planck\u0027s constant in one of the component algebras. This\napproach provides new insight into failures of various formalisms dealing with\nmixed quantum-classical systems. It shows that in the interacting mixed\nquantum-classical description, there can be no back-reaction of the quantum\nsystem on the classical. A natural algebraic requirement involving restriction\nof the tensor product of two quantum Hamilton algebras to their components\nproves that Planck\u0027s constant is unique.",
    "arxiv_id": "quant-ph/0301044",
    "authors": [
      "Debendranath Sahoo"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1088/0305-4470/37/3/031",
    "title": "Mixing quantum and classical mechanics and uniqueness of Planck\u0027s   constant",
    "url": "https://arxiv.org/abs/quant-ph/0301044"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fb8d782f-c767-4020-885b-4df506a4f475",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}