{
  "annotation_id": "9cc33a2b-1dc6-4ce9-ac54-7a495aaec983",
  "date_created": "2026-03-02T18:02:00.273000Z",
  "date_modified": "2026-03-02T18:02:00.273000Z",
  "file_hash": "353c1d0d866f8a1e30620bdcb3505eb80655ada7677e18d5a68496109a885a30",
  "private": false,
  "record": {
    "abstract": "A rigorous application of the correspondence rules shows that the operator of\nthe angular momentum of a quantum particle---corresponding to the classical\nmagnitude $\\mathbf{l}= m \\mathbf{r} \\wedge \\mathbf{v}$---is given by\n$\\mathbf{\\hat{l}}=\\mathbf{r}\\wedge(-i\\hbar\\mathbf{\\nabla}\n-\\frac{e}{c}\\mathbf{A})$ in the presence of an electromagnetic field. Thus,\ndespite the general opinion on the corresponding rules of quantization, the\neigenvalues of the angular momentum depend on the configuration of the\nelectromagnetic field. The usual rules of commutation\n$[{\\hat{l}}_i,{\\hat{l}}_j]=i\\hbar\\epsilon_{ijk}{\\hat{l}}_k$, that are at the\nfoundation of the calculus of angular momentum and of the theory of\n\\emph{spin}---and Bohm\u0027s example of the EPR argument---are not valid in the\npresence of an electromagnetic field. The expected value of the operator\n$\\mathbf{\\hat{l}}=-i\\hbar\\mathbf{r}\\wedge\\mathbf{\\nabla}$ is not gauge\ninvariant, it depends on the calibration of the electrodynamic potentials.",
    "arxiv_id": "quant-ph/0305049",
    "authors": [
      "O. Chavoya-Aceves"
    ],
    "categories": [
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "title": "Remarks on the Theory of Angular Momenta",
    "url": "https://arxiv.org/abs/quant-ph/0305049"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "139f6d85-95fc-41d2-a55c-47c92808101d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}