{
  "id": "0901.4293",
  "version": "v1",
  "published": "2009-01-27T17:36:34.000Z",
  "updated": "2009-01-27T17:36:34.000Z",
  "title": "Symmetry Reduction of Quasi-Free States",
  "authors": [
    "C. G. Torre"
  ],
  "comment": "18 pages",
  "categories": [
    "math-ph",
    "gr-qc",
    "hep-th",
    "math.MP"
  ],
  "abstract": "Given a group-invariant quasi-free state on the algebra of canonical commutation relations (CCR), we show how group averaging techniques can be used to obtain a symmetry reduced CCR algebra and reduced quasi-free state. When the group is compact this method of symmetry reduction leads to standard results which can be obtained using other methods. When the group is non-compact the group averaging prescription relies upon technically favorable conditions which we delineate. As an example, we consider symmetry reduction of the usual vacuum state for a Klein-Gordon field on Minkowski spacetime by a non-compact subgroup of the Poincar\\'e group consisting of a 1-parameter family of boosts, a 1-parameter family of spatial translations and a set of discrete translations. We show that the symmetry reduced CCR algebra and vacuum state correspond to that used by each of Berger, Husain, and Pierri for the polarized Gowdy ${\\bf T}^3$ quantum gravity model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-27T17:36:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "04.60.-m",
      "02.20.-a",
      "11.30.Cp",
      "11.10.Lm"
    ],
    "keywords": [
      "symmetry reduction",
      "symmetry reduced ccr algebra",
      "group-invariant quasi-free state",
      "group averaging prescription relies",
      "usual vacuum state"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.3131678",
      "journal": "Journal of Mathematical Physics",
      "year": 2009,
      "month": "Jun",
      "volume": 50,
      "number": 6,
      "pages": 2303
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 807230,
      "adsabs": "2009JMP....50f2303T"
    }
  }
}