{
  "annotation_id": "f09de3e2-d4ff-43c3-a273-2648b4474f79",
  "date_created": "2026-03-02T18:01:56Z",
  "date_modified": "2026-03-02T18:01:56Z",
  "file_hash": "dc3e0c716c37ef015d7a8bcc35600712dc742a4ff045328b1559d8b9f830f00b",
  "private": false,
  "record": {
    "abstract": "In this thesis we study several features of the operatorial approach to\nclassical mechanics pionereed by Koopman and von Neumann (KvN) in the Thirties.\nIn particular in the first part we study the role of the phases of the KvN\nstates. We analyze, within the KvN theory, the two-slit experiment and the\nAharonov-Bohm effect and we make a comparison between the classical and the\nquantum case. In the second part of the thesis we study the extension of the\nKvN formalism to the space of forms and Jacobi fields. We first show that all\nthe standard Cartan calculus on symplectic spaces can be performed via\nGrassmann variables or via suitable combinations of Pauli matrices. Second we\nstudy the extended Hilbert space of KvN which now includes forms and prove that\nit is impossible to have at the same time a positive definite scalar product\nand a unitary evolution. Clear physical reasons for this phenomenon are\nexhibited. We conclude the thesis with some work in progress on the issue of\nquantization.",
    "arxiv_id": "quant-ph/0301172",
    "authors": [
      "D. Mauro"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Topics in Koopman-von Neumann Theory",
    "url": "https://arxiv.org/abs/quant-ph/0301172"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "61bbf721-97a5-46ed-9f39-9a1b3c9a8221",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}