{
  "annotation_id": "e482eff6-534d-4bcf-bdfb-f9fb53b89cd3",
  "date_created": "2026-03-02T18:01:38.771000Z",
  "date_modified": "2026-03-02T18:01:38.771000Z",
  "file_hash": "460a90fe4c096b1f3e46a9b78b16004b1cfac1f7a6edd90f295ea91026601549",
  "private": false,
  "record": {
    "abstract": "Landau levels have represented a very rich field of research, which has\ngained widespread attention after their application to quantum Hall effect. In\na particular gauge, the holomorphic gauge, they give a physical implementation\nof Bargmann\u0027s Hilbert space of entire functions. They have also been recognized\nas a natural bridge between Feynman\u0027s path integral and Geometric Quantization.\nWe discuss here some mathematical subtleties involved in the formulation of the\nproblem when one tries to study quantum mechanics on a finite strip of sides\nL_1, L_2 with a uniform magnetic field and periodic boundary conditions. There\nis an apparent paradox here: infinitesimal translations should be associated to\ncanonical operators [p_x,p_y] \\propto i\\hslash B, and, at the same time, live\nin a Landau level of finite dimension B L_1L_2/(hc/e), which is impossible from\nWintner\u0027s theorem. The paper shows the way out of this conundrum.",
    "arxiv_id": "quant-ph/0007055",
    "authors": [
      "Enrico Onofri"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "journal_ref": "Int.J.Theor.Phys. 40 (2001) 537-549",
    "title": "Landau levels on a torus",
    "url": "https://arxiv.org/abs/quant-ph/0007055"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "83ba9aac-4838-4b25-ad0c-c8df53823660",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}