{
  "id": "1603.04371",
  "version": "v1",
  "published": "2016-03-14T18:06:31.000Z",
  "updated": "2016-03-14T18:06:31.000Z",
  "title": "Measures on Hilbert-Schmidt operators and algebraic quantum field theory",
  "authors": [
    "Svetoslav Zahariev"
  ],
  "comment": "18 pages",
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We present a general construction of non-Gaussian probability measures on the space of distributional kernels obeying a natural extension of the Osterwalder-Schrader axioms of Euclidean quantum field theory in arbitrary space-time dimension $d$. These measures may be interpreted as corresponding to scalar massive quantum fields with polynomial self-interaction. As a consequence, we obtain examples of non-free models satisfying the Haag-Kastler axioms of algebraic quantum field theory for arbitrary $d$. When $d<4$ we are able to transfer the measures to the space of distributions and verify the standard Osterwalder-Schrader axioms, hence, by a well-known reconstruction theorem, we also obtain quantum field theory models satisfying the axioms of Wightman.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-14T18:06:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81T05",
      "81T08"
    ],
    "keywords": [
      "algebraic quantum field theory",
      "hilbert-schmidt operators",
      "osterwalder-schrader axioms",
      "euclidean quantum field theory",
      "quantum field theory models satisfying"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160304371Z",
      "inspire": 1427469
    }
  }
}