{
  "id": "2310.03939",
  "version": "v1",
  "published": "2023-10-05T23:06:51.000Z",
  "updated": "2023-10-05T23:06:51.000Z",
  "title": "Integration-by-parts identities and differential equations for parametrised Feynman integrals",
  "authors": [
    "Daniele Artico",
    "Lorenzo Magnea"
  ],
  "comment": "22 pages + appendices, 4 figures",
  "categories": [
    "hep-ph",
    "hep-th"
  ],
  "abstract": "Integration-by-parts (IBP) identities and differential equations are the primary modern tools for the evaluation of high-order Feynman integrals. They are commonly derived and implemented in the momentum-space representation. We provide a different viewpoint on these important tools by working in Feynman-parameter space, and using its projective geometry. Our work is based upon little-known results pre-dating the modern era of loop calculations: we adapt and generalise these results, deriving a very general expression for sets of IBP identities in parameter space, associated with a generic Feynman diagram, and valid to any loop order, relying on the characterisation of Feynman-parameter integrands as projective forms. We validate our method by deriving and solving systems of differential equations for several simple diagrams at one and two loops, providing a unified perspective on a number of existing results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-05T23:06:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "differential equations",
      "parametrised feynman integrals",
      "integration-by-parts identities",
      "generic feynman diagram",
      "high-order feynman integrals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}