{
  "id": "1307.3052",
  "version": "v2",
  "published": "2013-07-11T10:55:21.000Z",
  "updated": "2014-03-20T09:49:24.000Z",
  "title": "A C*-algebra for quantized principal U(1)-connections on globally hyperbolic Lorentzian manifolds",
  "authors": [
    "Marco Benini",
    "Claudio Dappiaggi",
    "Thomas-Paul Hack",
    "Alexander Schenkel"
  ],
  "comment": "v2: 23 pages. Presentation improved and extended. New results (Theorem 4.9 and 5.2) on cohomological characterization of non-injective morphisms added. To appear in Comm. Math. Phys",
  "categories": [
    "math-ph",
    "hep-th",
    "math.DG",
    "math.MP"
  ],
  "abstract": "The aim of this work is to complete our program on the quantization of connections on arbitrary principal U(1)-bundles over globally hyperbolic Lorentzian manifolds. In particular, we show that one can assign via a covariant functor to any such bundle an algebra of observables which separates gauge equivalence classes of connections. The C*-algebra we construct generalizes the usual CCR-algebras since, contrary to the standard field-theoretic models, it is based on a presymplectic Abelian group instead of a symplectic vector space. We prove a no-go theorem according to which neither this functor, nor any of its quotients, satisfies the strict axioms of general local covariance. As a byproduct, we prove that a morphism violates the locality axiom if and only if a certain induced morphism of cohomology groups is non-injective. We then show that fixing any principal U(1)-bundle, there exists a suitable category of sub-bundles for which a quotient of our functor yields a quantum field theory in the sense of Haag and Kastler. We shall provide a physical interpretation of this feature and we obtain some new insights concerning electric charges in locally covariant quantum field theory.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-20T09:49:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81T20",
      "81T05",
      "81T13",
      "53Cxx"
    ],
    "keywords": [
      "globally hyperbolic lorentzian manifolds",
      "quantized principal",
      "locally covariant quantum field theory",
      "separates gauge equivalence classes",
      "presymplectic abelian group"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-014-2100-3",
      "journal": "Communications in Mathematical Physics",
      "year": 2014,
      "month": "Nov",
      "volume": 332,
      "number": 1,
      "pages": 477
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1242314,
      "adsabs": "2014CMaPh.332..477B"
    }
  }
}