标题： 诱导微分同胚在链上的L-无穷作用 显示英文标题

标题： On induced L-infinity action of diffeomorphisms on Cochains

摘要： 量子引力的一种方法是用德·拉姆代数来表述，选择时空的三角剖分，并将微分形式替换为上链（形成一个有限维向量空间）。广义相对论的关键问题是时空微分同胚对场的作用。在本文中，我们通过同伦转移（或等价地，BV积分）诱导微分同胚在上链上的作用，这导致了一个$L_{\infty}$作用。我们显式计算了当时空为区间、圆和正方形时的该作用。 显示英文摘要

摘要： 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.