{
  "id": "hep-th/9707040",
  "version": "v2",
  "published": "1997-07-03T08:12:08.000Z",
  "updated": "1998-04-10T23:58:44.000Z",
  "title": "Green functions of higher-order differential operators",
  "authors": [
    "Ivan G. Avramidi"
  ],
  "comment": "26 pages, LaTeX, 65 KB, no figures, some misprints and small mistakes are fixed, final version to appear in J. Math. Phys. (May, 1998)",
  "journal": "J.Math.Phys. 39 (1998) 2889-2909",
  "doi": "10.1063/1.532436",
  "categories": [
    "hep-th"
  ],
  "abstract": "The Green functions of the partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian manifold are investigated via the heat kernel methods. We study the resolvent of a special class of higher-order operators formed by the products of second-order operators of Laplace type defined with the help of a unique Riemannian metric but with different bundle connections and potential terms. The asymptotic expansion of the Green functions near the diagonal is studied in detail in any dimension. As a by-product a simple criterion for the validity of the Huygens principle is obtained. It is shown that all the singularities as well as the non-analytic regular parts of the Green functions of such high-order operators are expressed in terms of the usual heat kernel coefficients $a_k$ for a special Laplace type second-order operator.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1998-04-10T23:58:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "green functions",
      "higher-order differential operators",
      "special laplace type second-order operator",
      "usual heat kernel coefficients",
      "heat kernel methods"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "J. Math. Phys."
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 445207
    }
  }
}