{
  "id": "2307.11580",
  "version": "v1",
  "published": "2023-07-21T13:35:26.000Z",
  "updated": "2023-07-21T13:35:26.000Z",
  "title": "Wilson-Itô diffusions",
  "authors": [
    "Ismael Bailleul",
    "Ilya Chevyrev",
    "Massimiliano Gubinelli"
  ],
  "comment": "8 pages",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We introduce Wilson-It\\^o diffusions, a class of random fields on $\\mathbb{R}^d$ that change continuously along a scale parameter via a Markovian dynamics with local coefficients. Described via forward-backward stochastic differential equations, their observables naturally form a pre-factorization algebra \\`a la Costello-Gwilliam. We argue that this is a new non-perturbative quantization method applicable also to gauge theories and independent of a path-integral formulation. Whenever a path-integral is available, this approach reproduces the setting of Wilson-Polchinski flow equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-21T13:35:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diffusions",
      "wilson-polchinski flow equations",
      "forward-backward stochastic differential equations",
      "approach reproduces",
      "path-integral formulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}