位于边而不是点上的因果集上的电磁拉格朗日
Electromagnetic Lagrangian on a causal set that resides on edges rather than points
摘要：
本文的目标是引入一个版本的电磁拉格朗日因果集的方式，将解决非局部性问题固有的因果集理论。其关键思想是拉格朗日密度被分配给边缘而不是点，并且有一种方法可以定义给定边缘的“相邻边缘”的概念，使得每个边缘只有1000个相邻边缘，这最终允许理论是局部的。这与每个点都有无限多个直接邻居的点形成对比，这是非局部性的来源。无论如何，为了定义电磁拉格朗日量，都需要边缘，而不考虑局部性;本文的新颖之处在于将拉格朗日密度也分配给边缘。此外，在其他文件的边缘都是类空间和类时间，而在本文中，他们只是类时间。这使得计算变得相当复杂，但它在保持局部性方面至关重要，因为只有当边缘是类时的时候，垂直于边缘的超平面中的洛伦兹群才是紧的。
英文摘要：
The goal of this paper is to introduce one of the versions of the electromagnetic Lagrangian on a causal set in such a way that would address the non-locality issues inherent to causal set theory. The key idea is that Lagrangian density is assigned to the edges rather than points, and there is a way of defining the concept of "neighboring edges" of a given edge in such a way that each edge has only finitely many neighboring edges which would ultimately allow for the theory to be local. That is to be contrasted with points where every point has infinitely many direct neighbors which is a source of non-locality. The edges are needed in order to define electromagnetic Lagrangian anyway, regardless of the consideration of locality; the novelty of this paper is to assign Lagrangian density to the edges as well. Also, in the other papers edges were both spacelike and timelike, while in this paper they are only timelike. This makes calculations considerably more complicated, but it is crucial in preserving locality since the Lorentz group in a hyperplane perpendicular to the edge is compact only if the edge is timelike.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
