{
  "id": "1403.7253",
  "version": "v2",
  "published": "2014-03-28T00:20:38.000Z",
  "updated": "2014-11-25T21:25:15.000Z",
  "title": "A renormalisation group method. II. Approximation by local polynomials",
  "authors": [
    "David C. Brydges",
    "Gordon Slade"
  ],
  "comment": "30 pages",
  "categories": [
    "math-ph",
    "math.DS",
    "math.MP",
    "math.PR"
  ],
  "abstract": "This paper is the second in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. The method is set within a normed algebra $\\mathcal{N}$ of functionals of the fields. In this paper, we develop a general method---localisation---to approximate an element of $\\mathcal{N}$ by a local polynomial in the fields. From the point of view of the renormalisation group, the construction of the local polynomial corresponding to $F$ in $\\mathcal{N}$ amounts to the extraction of the relevant and marginal parts of $F$. We prove estimates relating $F$ and its corresponding local polynomial, in terms of the $T_{\\phi}$ semi-norm introduced in part I of the series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-28T00:20:38.000Z",
      "abstract": "This paper is the second in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. The method is set within a normed algebra $\\mathcal{N}$ of functionals of the fields. In this paper, we develop a general method---localisation---to approximate an element of $\\mathcal{N}$ by a local polynomial in the fields. From the point of view of the renormalisation group, the construction of the local polynomial corresponding to $F \\in \\mathcal{N}$ amounts to the extraction of the relevant and marginal parts of $F$. We prove estimates relating $F$ and its corresponding local polynomial, in terms of the $T_\\phi$ semi-norm introduced in part~I of the series.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-25T21:25:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B28",
      "97K99",
      "37A60"
    ],
    "keywords": [
      "approximation",
      "lattice field theories",
      "general method-localisation-to approximate",
      "rigorous renormalisation group method",
      "fermion fields"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s10955-014-1164-y",
      "journal": "Journal of Statistical Physics",
      "year": 2015,
      "month": "May",
      "pages": 461,
      "volume": 159,
      "number": 3
    },
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1287822,
      "adsabs": "2015JSP...159..461B"
    }
  }
}