{
  "id": "0902.3833",
  "version": "v5",
  "published": "2009-02-23T01:05:37.000Z",
  "updated": "2011-08-03T18:53:54.000Z",
  "title": "Towards a gauge theory for evolution equations on vector-valued spaces",
  "authors": [
    "Stefano Cardanobile",
    "Delio Mugnolo"
  ],
  "comment": "8 pages",
  "journal": "J.Math.Phys.50:103520,2009",
  "doi": "10.1063/1.3227666",
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We investigate symmetry properties of vector-valued diffusion and Schr\\\"odinger equations. For a separable Hilbert space $H$ we characterize the subspaces of $L^2(\\Omega, H)$ that are local (i.e., defined pointwise) and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge symmetries in mathematical physics is explored.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2011-08-03T18:53:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E40",
      "47B65",
      "53C80",
      "03.65.Fd",
      "02.10.Ud",
      "02.30.Hq",
      "05.60.-k",
      "03.65.Ge"
    ],
    "keywords": [
      "evolution equations",
      "gauge theory",
      "vector-valued spaces",
      "symmetry properties",
      "separable hilbert space"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 2009,
      "month": "Oct",
      "volume": 50,
      "number": 10,
      "pages": 3520
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 814012,
      "adsabs": "2009JMP....50j3520C"
    }
  }
}