{
  "id": "2207.08555",
  "version": "v1",
  "published": "2022-07-18T12:22:10.000Z",
  "updated": "2022-07-18T12:22:10.000Z",
  "title": "Perturbation theory for the $Φ^4_3$ measure, revisited with Hopf algebras",
  "authors": [
    "Nils Berglund",
    "Tom Klose"
  ],
  "comment": "24 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR",
    "quant-ph"
  ],
  "abstract": "We give a relatively short, almost self-contained proof of the fact that the partition function of the suitably renormalised $\\Phi^4_3$ measure admits an asymptotic expansion, the coefficients of which converge as the ultraviolet cut-off is removed. We also examine the question of Borel summability of the asymptotic series. The proofs are based on Wiener chaos expansions, Hopf-algebraic methods, and bounds on the value of Feynman diagrams obtained through BPHZ renormalisation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-18T12:22:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35R11",
      "81T17",
      "82C28"
    ],
    "keywords": [
      "hopf algebras",
      "perturbation theory",
      "wiener chaos expansions",
      "feynman diagrams",
      "hopf-algebraic methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}