{
  "annotation_id": "dd0e842a-a20a-46d1-bdc9-cd873a837fd9",
  "date_created": "2026-03-02T18:02:40.782000Z",
  "date_modified": "2026-03-02T18:02:40.782000Z",
  "file_hash": "b18c4cc77270be720991e20094da73cbdb09c1811cb70eb6989cf145d0841009",
  "private": false,
  "record": {
    "abstract": "We consider quasi-free stochastically positive ground and thermal states on\nWeyl algebras in Euclidean time formulation. In particular, we obtain a new\nderivation of a general form of thermal quasi-free state and give conditions\nwhen such state is stochastically positive i.e. when it defines periodic\nstochastic process with respect to Euclidean time, so called thermal process.\nThen we show that thermal process completely determines modular structure\ncanonically associated with quasi-free state on Weyl algebra. We discuss a\nvariety of examples connected with free field theories on globally hyperbolic\nstationary space-times and models of quantum statistical mechanics.",
    "arxiv_id": "quant-ph/9704039",
    "authors": [
      "R. Gielerak",
      "L. Jakobczyk",
      "R. Olkiewicz"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.532639",
    "journal_ref": "J.Math.Phys. 39 (1998) 6291-6328",
    "title": "Stochastically positive structures on Weyl algebras. The case of   quasi-free states",
    "url": "https://arxiv.org/abs/quant-ph/9704039"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6205e84f-9a0a-4918-8234-7f011f8f60f9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}