{
  "annotation_id": "e867e5ca-57a9-496a-9ff7-9303975468b9",
  "date_created": "2026-03-02T18:01:11.170000Z",
  "date_modified": "2026-03-02T18:01:11.170000Z",
  "file_hash": "9305c86dbb9d10e1257951c254ad40e803c63db9c041f6025c959e515f7fa665",
  "private": false,
  "record": {
    "abstract": "It is noted that a given pairing of the phase factor and gauge transformation\nto retain gauge symmetry is not unique. In their seminal paper, when Yang and\nMills (YM) discuss the phase factor - gauge transformation relationship, they\ncite Pauli\u0027s review paper. It is interesting that although Pauli in that paper\npresents the electromagnetic field strength in terms of a commutator, for\nwhatever reason YM did not extrapolate the commutator\u0027s use to obtain the\nYang-Mills field strength -- they obtained it by trial and error. Presented is\na derivation of this field strength using the commutator approach detailing how\ncertain terms cancel each other. Finally, the Yang-Mills field transformation\nis derived in a slightly different way than is traditionally done.",
    "arxiv_id": "physics/0609084",
    "authors": [
      "Samuel L. Marateck"
    ],
    "categories": [
      "physics.hist-ph",
      "math-ph",
      "math.MP"
    ],
    "title": "Yang-Mills redux",
    "url": "https://arxiv.org/abs/physics/0609084"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "534b9d6f-1be3-4498-a95d-53e0e811bb0d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}