{
  "annotation_id": "d85cba46-4271-4121-9184-52c4efdad007",
  "date_created": "2026-03-02T18:01:53.102000Z",
  "date_modified": "2026-03-02T18:01:53.102000Z",
  "file_hash": "e96f92f268e8f91acdd438d994fcf4754aea05590787dcc2ae1d6ceec66d255d",
  "private": false,
  "record": {
    "abstract": "In this paper we analyze two different functional formulations of classical\nmechanics. In the first one the Jacobi fields are represented by bosonic\nvariables and belong to the vector (or its dual) representation of the\nsymplectic group. In the second formulation the Jacobi fields are given as\ncondensates of Grassmannian variables belonging to the spinor representation of\nthe metaplectic group. For both formulations we shall show that, differently\nfrom what happens in the case presented in paper no. (I), it is possible to\nendow the associated Hilbert space with a positive definite scalar product and\nto describe the dynamics via a Hermitian Hamiltonian. The drawback of this\nformulation is that higher forms do not appear automatically and that the\ndescription of chaotic systems may need a further extension of the Hilbert\nspace.",
    "arxiv_id": "quant-ph/0208047",
    "authors": [
      "E. Deotto",
      "E. Gozzi",
      "D. Mauro"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "doi": "10.1063/1.1623334",
    "journal_ref": "J.Math.Phys. 44 (2003) 5937-5957",
    "title": "Hilbert Space Structure in Classical Mechanics: (II)",
    "url": "https://arxiv.org/abs/quant-ph/0208047"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "586064fe-f716-4593-b4b5-a408b8d42db3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}