{
  "annotation_id": "0fb3e496-f717-4c6d-b8ea-159cbc4d26fd",
  "date_created": "2026-03-02T18:02:24.059000Z",
  "date_modified": "2026-03-02T18:02:24.059000Z",
  "file_hash": "373627d942211d0445996707ad9a962baba1cbf69e2b39c4466e278d6858a8ed",
  "private": false,
  "record": {
    "abstract": "We develop a prequantum classical statistical model in that the role of\nhidden variables is played by classical (vector) fields. We call this model\nPrequantum Classical Statistical Field Theory (PCSFT). The correspondence\nbetween classical and quantum quantities is asymptotic, so we call our approach\nasymptotic dequantization. In this note we pay the main attention to\ninterpretation of so called pure quantum states (wave functions) in PCSFT,\nespecially stationary states. We show, see Theorem 2, that pure states of QM\ncan be considered as labels for Gaussian measures concentrated on one\ndimensional complex subspaces of phase space that are invariant with respect to\nthe Schr\\\"odinger dynamics. ``A quantum system in a stationary state $\\psi$\u0027\u0027\nin PCSFT is nothing else than a Gaussian ensemble of classical fields\n(fluctuations of the vacuum field of a very small magnitude) which is not\nchanged in the process of Schr\\\"odinger\u0027s evolution. We interpret in this way\nthe problem of {\\it stability of hydrogen atom.",
    "arxiv_id": "quant-ph/0601174",
    "authors": [
      "Andrei Khrennikov"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Interpretation of Stationary States in Prequantum Classical Statistical   Field Theory",
    "url": "https://arxiv.org/abs/quant-ph/0601174"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bdaddce8-3d80-45f6-baac-3c12a0319deb",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}