{
  "annotation_id": "307fa7bb-4a40-44d5-9f9b-bceb34a4fd5a",
  "date_created": "2026-03-02T18:02:41.599000Z",
  "date_modified": "2026-03-02T18:02:41.599000Z",
  "file_hash": "b20ff509f7a5f88aaf8d2b0468acdb85a02f9ce0a6692112fd81f3a9a4d6f2f6",
  "private": false,
  "record": {
    "abstract": "Nonlinear Doebner-Goldin [Phys. Rev. A 54, 3764 (1996)] gauge transformations\n(NGT) defined in terms of a wave function $\\psi(x)$ do not form a group. To get\na group property one has to consider transformations that act differently on\ndifferent branches of the complex argument function and the knowledge of the\nvalue of $\\psi(x)$ is not sufficient for a well defined NGT. NGT that are well\ndefined in terms of $\\psi(x)$ form a semigroup parametrized by a real number\n$\\gamma$ and a nonzero $\\lambda$ which is either an integer or $-1\\leq\n\\lambda\\leq 1$. An extension of NGT to projectors and general density matrices\nleads to NGT with complex $\\gamma$. Both linearity of evolution and Hermiticity\nof density matrices are gauge dependent properties.",
    "arxiv_id": "quant-ph/9711053",
    "authors": [
      "Marek Czachor"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.57.R2263",
    "journal_ref": "Phys.Rev. A57 (1998) 2263",
    "title": "Structure of nonlinear gauge transformations",
    "url": "https://arxiv.org/abs/quant-ph/9711053"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "130c8597-787c-49a8-a824-41ad38891222",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}