{
  "annotation_id": "da1a941b-6b16-4920-83b6-8059563efc9b",
  "date_created": "2026-03-02T18:01:52.363000Z",
  "date_modified": "2026-03-02T18:01:52.363000Z",
  "file_hash": "c98ebf2ef282c58d1592bd9d889b14bca0d518ee0e5c8bfc4a8cd69cb67a34e0",
  "private": false,
  "record": {
    "abstract": "A necessary and sufficient condition for Pauli\u0027s spin-statistics relation is\ngiven for nonrelativistic anyons, bosons, and fermions in two and three spatial\ndimensions.\n  For any point particle species in two spatial dimensions, denote by J the\ntotal (i.e., spin plus orbital) angular momentum of a single particle, and\ndenote by j the total angular momentum of the corresponding two-particle system\nwith respect to its center of mass. In three spatial dimensions, write J_z and\nj_z for the z-components of these vector operators.\n  In two spatial dimensions, the spin statistics connection holds if and only\nif there exists a unitary operator U such that j=2UJU^*. In three dimensions,\nthe analogous relation cannot hold as it stands, but restricting it to an\nappropriately chosen subspace of the state space yields a sufficient and\nnecessary condition for the spin-statistics connection.",
    "arxiv_id": "quant-ph/0208151",
    "authors": [
      "Bernd Kuckert"
    ],
    "categories": [
      "quant-ph",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1016/j.physleta.2003.12.051",
    "journal_ref": "Phys.Lett.A322:47-53,2004",
    "title": "Spin \u0026 Statistics in Nonrelativistic Quantum Mechanics, I",
    "url": "https://arxiv.org/abs/quant-ph/0208151"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "59a33314-a2c9-4b0a-a13b-4c29ec03ba8a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}