{
  "id": "1911.03099",
  "version": "v1",
  "published": "2019-11-08T07:22:11.000Z",
  "updated": "2019-11-08T07:22:11.000Z",
  "title": "On the Lévy-Leblond-Newton equation and its symmetries: a geometric view",
  "authors": [
    "Serge Lazzarini",
    "Loïc Marsot"
  ],
  "comment": "24 pages, 2 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The L\\'evy-Leblond-Newton (LLN) equation for non-relativistic fermions with a gravitational self-interaction is reformulated within the framework of a Bargmann structure over a $(n+1)$-dimensional Newton-Cartan (NC) spacetime. The Schr\\\"odinger-Newton (SN) group, introduced in [21] as the maximal group of invariance of the SN equation, turns out to be also the group of conformal Bargmann automorphisms preserving the coupled L\\'evy-Leblond and NC gravitational field equations. Within the Bargmann geometry a generalization of the LLN equation is provided as well. The canonical projective unitary representation of the SN group on 4-component spinors is also presented. In particular, when restricted to dilations, the value of the dynamical exponent $z=(n+2)/3$ is recovered as previously derived in [21] for the SN equation. Subsequently, conserved quantities associated to the (generalized) LLN equation are also exhibited.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-08T07:22:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric view",
      "lévy-leblond-newton equation",
      "lln equation",
      "symmetries",
      "nc gravitational field equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}