{
  "annotation_id": "113770a6-10d6-4fcf-97ea-d1c6396a4830",
  "date_created": "2026-03-02T18:02:16.364000Z",
  "date_modified": "2026-03-02T18:02:16.364000Z",
  "file_hash": "55393f74cc56a3ca352cb83b5b11f1c401097ef43d210472dec83b07a3c7fe59",
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  "record": {
    "abstract": "The phase space $S\\times Z$ for a particle on a circle is considered.\nDisplacement operators in this phase space are introduced and their properties\nare studied. Wigner and Weyl functions in this context are also considered and\ntheir physical interpretation and properties are discussed. All results are\ncompared and contrasted with the corresponding ones for the harmonic oscillator\nin the $R \\times R$ phase space.",
    "arxiv_id": "quant-ph/0504015",
    "authors": [
      "S. Zhang",
      "A. Vourdas"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1616997",
    "journal_ref": "J. Math. Phys. 44 (2003) 5084-5094",
    "title": "Phase space methods for particles on a circle",
    "url": "https://arxiv.org/abs/quant-ph/0504015"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "303768e3-c2c3-4029-8ae2-82d3ba0cea16",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}