{
  "id": "quant-ph/0305049",
  "version": "v4",
  "published": "2003-05-09T19:10:35.000Z",
  "updated": "2013-09-07T00:24:22.000Z",
  "title": "Remarks on the Theory of Angular Momenta",
  "authors": [
    "O. Chavoya-Aceves"
  ],
  "comment": "Detail is included to make it easier to follow the mathematical arguments, in particular for eqs. 25 and 26 (19 and 20 in the previous version); minor stylistic corrections are also included",
  "categories": [
    "quant-ph"
  ],
  "abstract": "A rigorous application of the correspondence rules shows that the operator of the angular momentum of a quantum particle---corresponding to the classical magnitude $\\mathbf{l}= m \\mathbf{r} \\wedge \\mathbf{v}$---is given by $\\mathbf{\\hat{l}}=\\mathbf{r}\\wedge(-i\\hbar\\mathbf{\\nabla} -\\frac{e}{c}\\mathbf{A})$ in the presence of an electromagnetic field. Thus, despite the general opinion on the corresponding rules of quantization, the eigenvalues of the angular momentum depend on the configuration of the electromagnetic field. The usual rules of commutation $[{\\hat{l}}_i,{\\hat{l}}_j]=i\\hbar\\epsilon_{ijk}{\\hat{l}}_k$, that are at the foundation of the calculus of angular momentum and of the theory of \\emph{spin}---and Bohm's example of the EPR argument---are not valid in the presence of an electromagnetic field. The expected value of the operator $\\mathbf{\\hat{l}}=-i\\hbar\\mathbf{r}\\wedge\\mathbf{\\nabla}$ is not gauge invariant, it depends on the calibration of the electrodynamic potentials.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-09-07T00:24:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "electromagnetic field",
      "angular momentum depend",
      "usual rules",
      "electrodynamic potentials",
      "gauge invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003quant.ph..5049C"
    }
  }
}