{
  "id": "0708.0677",
  "version": "v1",
  "published": "2007-08-05T16:43:44.000Z",
  "updated": "2007-08-05T16:43:44.000Z",
  "title": "Observables IV: The presheaf perspective",
  "authors": [
    "Hans F. de Groote"
  ],
  "comment": "35 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.OA",
    "quant-ph"
  ],
  "abstract": "In this fourth of our series of papers on observables we show that one can associate to each von Neumann algebra R a pair of isomorphic presheaves, the upper presheaf O^{+}_{R} and the lower presheaf O^{-}_{R}, on the category of abelian von Neumann subalgebras of R. Each $A \\in R_{sa}$ induces a global section of O^{+}_{R} and of O^{-}_{R} respectively. We call them \\emph {contextual observables}. But we show that, in general, not every global section of these presheaves arises in this way. Moreover, we discuss states of a von Neumann algebra in the presheaf context.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-05T16:43:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "von neumann algebra",
      "presheaf perspective",
      "global section",
      "abelian von neumann subalgebras",
      "lower presheaf"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.0677D"
    }
  }
}