{
  "id": "1809.03399",
  "version": "v1",
  "published": "2018-09-10T15:31:39.000Z",
  "updated": "2018-09-10T15:31:39.000Z",
  "title": "The number of master integrals as Euler characteristic",
  "authors": [
    "Thomas Bitoun",
    "Christian Bogner",
    "René Pascal Klausen",
    "Erik Panzer"
  ],
  "comment": "Contribution to the proceedings of Loops and Legs in Quantum Field Theory (LL2018), 29 April - 04 May 2018, St. Goar (Germany)",
  "categories": [
    "hep-th"
  ],
  "abstract": "We give a brief introduction to a parametric approach for the derivation of shift relations between Feynman integrals and a result on the number of master integrals. The shift relations are obtained from parametric annihilators of the Lee-Pomeransky polynomial $\\mathcal{G}$. By identification of Feynman integrals as multi-dimensional Mellin transforms, we show that this approach generates every shift relation. Feynman integrals of a given family form a vector space, whose finite dimension is naturally interpreted as the number of master integrals. This number is an Euler characteristic of the polynomial $\\mathcal{G}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-10T15:31:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "master integrals",
      "euler characteristic",
      "feynman integrals",
      "shift relation",
      "multi-dimensional mellin transforms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}