{
  "id": "2207.14390",
  "version": "v1",
  "published": "2022-07-27T05:05:27.000Z",
  "updated": "2022-07-27T05:05:27.000Z",
  "title": "About non-relativistic quantum mechanics and electromagnetism",
  "authors": [
    "Ladislaus Alexander Bányai",
    "Mircea Bundaru"
  ],
  "comment": "19 pages, 3 figures",
  "categories": [
    "quant-ph",
    "cond-mat.other"
  ],
  "abstract": "We describe here the coherent formulation of electromagnetism in the non-relativistic quantum-mechanical many-body theory of interacting charged particles. We use the mathematical frame of the field theory and its quantization in the spirit of the QED. This is necessary because a manifold of misinterpretations emerged especially regarding the magnetic field and gauge invariance. The situation was determined by the historical development of quantum mechanics, starting from the Schr\\\"odinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions. Our approach to the non-relativistic QED emphasizes the role of the gauge-invariance and of the external fields. We develop further the $1/c^2$ approximation of this theory allowing a closed description of the interacting charged particles without photons. The resulting Hamiltonian coincides with the quantized version of the Darwin Hamiltonian containing besides the Coulomb also a current-current diamagnetic interaction. We show on some examples the importance of this extension of the many-body theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-27T05:05:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-relativistic quantum mechanics",
      "electromagnetism",
      "interacting charged particles",
      "non-relativistic quantum-mechanical many-body theory",
      "current-current diamagnetic interaction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}