{
  "id": "1504.05042",
  "version": "v1",
  "published": "2015-04-20T13:02:04.000Z",
  "updated": "2015-04-20T13:02:04.000Z",
  "title": "On the Schr{ö}dinger -Newton equation and its symmetries: a geometric view",
  "authors": [
    "C Duval",
    "Serge Lazzarini"
  ],
  "comment": "LaTeX 28 pages",
  "categories": [
    "math-ph",
    "gr-qc",
    "hep-th",
    "math.MP"
  ],
  "abstract": "The Schr{\\\"o}dinger-Newton (SN) equation is recast on purely geometrical grounds, namely in terms of Bargmann structures over (n + 1)-dimensional Newton-Cartan (NC) spacetimes. Its maximal group of invariance, which we call the SN group, is determined as the group of conformal Bargmann automorphisms that preserve the coupled Schr{\\\"o}dinger and NC gravitational field equations. Canonical unitary representations of the SN group are worked out, helping us recover, in particular, a very specific occurrence of dilations with dynamical exponent z = (n + 2)/3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-20T13:02:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "newton equation",
      "geometric view",
      "sn group",
      "symmetries",
      "nc gravitational field equations"
    ],
    "publication": {
      "doi": "10.1088/0264-9381/32/17/175006",
      "journal": "Classical and Quantum Gravity",
      "year": 2015,
      "month": "Sep",
      "volume": 32,
      "number": 17,
      "pages": 175006
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015CQGra..32q5006D",
      "inspire": 1362172
    }
  }
}