{
  "annotation_id": "c67c9958-9488-456b-b460-3f61e084ab7f",
  "date_created": "2026-03-02T18:01:51.780000Z",
  "date_modified": "2026-03-02T18:01:51.780000Z",
  "file_hash": "d8dfd5e34f5a2ddeb8b566269c515d3451d5f0d31dcfa6a81517bd2e576ede53",
  "private": false,
  "record": {
    "abstract": "The direct and indirect Lagrangian representations of the planar harmonic\noscillator have been discussed. The reduction of these Lagrangians in their\nbasic forms characterising either chiral, or pseudo - chiral oscillators have\nbeen given. A Hamiltonian analysis, showing its equivalence with the Lagrangian\nformalism has also been provided. Finally, we show that the chiral and pseudo -\nchiral modes act as dynamical structures behind the Jordan - Schwinger\nrealizations of the SU(2) and SU(1,1) algebras. Also, the SU(1,1) construction\nfound here is different from the standard Jordan - Schwinger form.",
    "arxiv_id": "quant-ph/0205143",
    "authors": [
      "Rabin Banerjee",
      "Pradip Mukherjee"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "title": "The Harmonic Oscillator in the Plane and the Jordan-Schwinger Algebras",
    "url": "https://arxiv.org/abs/quant-ph/0205143"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d418f5a0-1763-4de5-b948-f4678096ba68",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}