{
  "id": "1309.5639",
  "version": "v2",
  "published": "2013-09-22T19:38:42.000Z",
  "updated": "2013-10-17T11:23:37.000Z",
  "title": "Independence Conditions for Nets of Local Algebras as Sheaf Conditions",
  "authors": [
    "Sander A. M. Wolters",
    "Hans Halvorson"
  ],
  "comment": "34 pages, 0 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We apply constructions from topos-theoretic approaches to quantum theory to algebraic quantum ?eld theory. Thus a net of operator algebras is reformulated as a functor that maps regions of spacetime into a category of ringed topoi. We ask whether this functor is a sheaf, a question which is related to the net satisfying certain kinematical independence conditions. In addition, we consider a C*-algebraic version of Nuiten's recent sheaf condition, and demonstrate how it relates to C*-independence of the underlying net of operator algebras.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-17T11:23:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sheaf condition",
      "local algebras",
      "operator algebras",
      "topos-theoretic approaches",
      "kinematical independence conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.5639W"
    }
  }
}