{
  "id": "1908.06790",
  "version": "v1",
  "published": "2019-08-19T13:23:46.000Z",
  "updated": "2019-08-19T13:23:46.000Z",
  "title": "From Classical Trajectories to Quantum Commutation Relations",
  "authors": [
    "Florio M. Ciaglia",
    "Giuseppe Marmo",
    "Luca Schiavone"
  ],
  "comment": "25 pages. Comments are welcome!",
  "journal": "Springer Proceedings in Physics, volume 229, 2019",
  "doi": "10.1007/978-3-030-24748-5_9",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian description because of the Noether theorem and because they are the starting point for the quantization. As a matter of fact many ambiguities arise in each step of such a reconstruction which must be solved by the ingenuity of the theoretician. In the present work we describe geometric structures emerging in Lagrangian, Hamiltonian and Quantum description of a dynamical system underlining how many of them are not really fixed only by the trajectories observed by the experimentalist.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-19T13:23:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum commutation relations",
      "classical trajectories",
      "differential equations",
      "dynamical system",
      "translate experimental data"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}