{
  "id": "0909.4122",
  "version": "v3",
  "published": "2009-09-23T02:41:11.000Z",
  "updated": "2015-10-19T14:53:10.000Z",
  "title": "The geometric $β$-function in curved space-time under operator regularization",
  "authors": [
    "Susama Agarwala"
  ],
  "comment": "20 pages",
  "journal": "Journal of Mathematical Physics, 2015, vol 56, issue 6",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, I compare the generators of the renormalization group flow, or the geometric $\\beta$-functions for dimensional regularization and operator regularization. I then extend the analysis to show that the geometric $\\beta$-function for a scalar field theory on a closed compact Riemannian manifold is defined on the entire manifold. I then extend the analysis to find the generator of the renormalization group flow for a conformal scalar-field theories on the same manifolds. The geometric $\\beta$-function in this case is not defined.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-07T06:17:59.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-10-19T14:53:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "operator regularization",
      "curved space-time",
      "renormalization group flow",
      "closed compact riemannian manifold",
      "conformal scalar-field theories"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "J. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 832106,
      "adsabs": "2009arXiv0909.4122A"
    }
  }
}