{
  "id": "2004.04622",
  "version": "v1",
  "published": "2020-04-09T16:10:21.000Z",
  "updated": "2020-04-09T16:10:21.000Z",
  "title": "Cartan Connection for Schrödinger equation. The nature of vacuum",
  "authors": [
    "Radosław A. Kycia"
  ],
  "comment": "14 pages",
  "categories": [
    "math-ph",
    "math.AP",
    "math.DG",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "Cartan connection arising from the scaling group of the wave function for the Schr\\\"{o}dinger equation will be presented. This geometric object will be interpreted as a background (vacuum) on which the system evolves. The idea is the generalization of concepts present in de Broglie-Bohm (pilot wave) theory. The connection allows investigating the geometry of the space on which this Schr\\\"{o}dinger-Cartan connection is constructed. The procedure is general enough for constructing (non-uniquely) torsion-free Cartan connections for general Partial Differential Equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-09T16:10:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "schrödinger equation",
      "general partial differential equations",
      "torsion-free cartan connections",
      "wave function",
      "geometric object"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}