{
  "annotation_id": "2d740cde-3080-41c3-8e61-1196e77ca552",
  "date_created": "2026-03-02T18:02:16.807000Z",
  "date_modified": "2026-03-02T18:02:16.807000Z",
  "file_hash": "e39b9ab14739e439bcd38f5036ae0449e3a91fb76412eaae31acbf60db634c47",
  "private": false,
  "record": {
    "abstract": "The concept of the Schwinger Representation of a finite or compact simple Lie\ngroup is set up as a multiplicity-free direct sum of all the unitary\nirreducible representations of the group. This is abstracted from the\nproperties of the Schwinger oscillator construction for SU(2), and its\nrelevance in several quantum mechanical contexts is highlighted. The Schwinger\nrepresentations for $SU(2), SO(3)$ and SU(n) for all $n$ are constructed via\nspecific carrier spaces and group actions. In the SU(2) case connections to the\noscillator construction and to Majorana\u0027s theorem on pure states for any spin\nare worked out. The role of the Schwinger Representation in setting up the\nWigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group is\nbrought out.",
    "arxiv_id": "quant-ph/0505012",
    "authors": [
      "S. Chaturvedi",
      "G. Marmo",
      "N. Mukunda",
      "R. Simon",
      "A. Zampini"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "doi": "10.1142/S0129055X06002802",
    "journal_ref": "Rev.Math.Phys. 18 (2006) 887-912",
    "title": "The Schwinger Representation of a Group: Concept and Applications",
    "url": "https://arxiv.org/abs/quant-ph/0505012"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0b39912e-1500-4722-80f8-689ee1022a77",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}