{
  "id": "2406.17922",
  "version": "v1",
  "published": "2024-06-25T20:09:40.000Z",
  "updated": "2024-06-25T20:09:40.000Z",
  "title": "On induced L-infinity action of diffeomorphisms on Cochains",
  "authors": [
    "Andrey Losev",
    "Dmitrii Sheptunov",
    "Xin Geng"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "One of the approaches to quantum gravity is to formulate it in terms of De Rham algebra, choose a triangulation of space-time, and replace differential forms by cochains (that form a finite dimensional vector space). The key issue of general relativity is the action of diffeomorphisms of space-time on fields. In this paper, we induce the action of diffeomorphisms on cochains by homotopy transfer (or, equivalently, BV integral) that leads to a $L_{\\infty}$ action. We explicitly compute this action for the space-time being an interval, a circle, and a square.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-25T20:09:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "induced l-infinity action",
      "diffeomorphisms",
      "finite dimensional vector space",
      "space-time",
      "replace differential forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}