{
  "id": "2205.09223",
  "version": "v1",
  "published": "2022-05-18T21:44:21.000Z",
  "updated": "2022-05-18T21:44:21.000Z",
  "title": "Local operators in the Sine-Gordon model: $\\partial_μφ\\, \\partial_νφ$ and the stress tensor",
  "authors": [
    "Markus B. Fröb",
    "Daniela Cadamuro"
  ],
  "comment": "57 pages in CMP style",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "We consider the simplest non-trivial local composite operators in the massless Sine-Gordon model, which are $\\partial_\\mu \\phi \\, \\partial_\\nu \\phi$ and the stress tensor $T_{\\mu\\nu}$. We show that even in the finite regime $\\beta^2 < 4 \\pi$ of the theory, these operators need additional renormalisation (beyond the free-field normal-ordering) at each order in perturbation theory. We further prove convergence of the renormalised perturbative series for their expectation values, both in the Euclidean signature and in Minkowski space-time, and for the latter in an arbitrary Hadamard state. Lastly, we show that one must add a quantum correction (proportional to $\\hbar$) to the renormalised stress tensor to obtain a conserved quantity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-18T21:44:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local operators",
      "simplest non-trivial local composite operators",
      "arbitrary hadamard state",
      "operators need additional renormalisation",
      "renormalised stress tensor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 57,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}