{
  "id": "2108.11312",
  "version": "v1",
  "published": "2021-08-25T16:25:47.000Z",
  "updated": "2021-08-25T16:25:47.000Z",
  "title": "An SPDE approach to perturbation theory of $Φ^4_2$: asymptoticity and short distance behavior",
  "authors": [
    "Hao Shen",
    "Rongchan Zhu",
    "Xiangchan Zhu"
  ],
  "comment": "36 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "In this paper we study the perturbation theory of $\\Phi^4_2$ model on the whole plane via stochastic quantization. We use integration by parts formula (i.e. Dyson-Schwinger equations) to generate the perturbative expansion for the $k$-point correlation functions, and prove bounds on the remainder of the truncated expansion using PDE estimates; this in particular proves that the expansion is asymptotic. Furthermore, we derive short distance behaviors of the $2$-point function and the connected $4$-point function, also via suitable Dyson-Schwinger equations combined with PDE arguments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-25T16:25:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perturbation theory",
      "spde approach",
      "dyson-schwinger equations",
      "asymptoticity",
      "point function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}