协变相空间上作为Dirac算子的Barnich-Troessaert算子
Barnich-Troessaert Bracket as a Dirac Bracket on the Covariant Phase Space
摘要：
Barnich-Troessaert括号是广义相对论协变相空间上的一个修正泊松括号。新的括号允许我们计算电荷，否则这些电荷是不可积的。然而，这里有一个陷阱。有一个明确的规定，如何评估任何这样的费用的新括号，但鲜为人知的是如何扩展到整个相空间的括号。这是一个问题，因为不是每一个引力可观测量也是一个电荷。在本文中，我们提出了这样的扩展。其基本思想是从协变相空间中去除辐射数据。这需要二级约束。给出一些基本的假设，我们表明，由此产生的狄拉克括号上的约束曲面是什么，但BT括号。一个启发式的论点，表明所得到的约束曲面只能包含重力边缘模式。
英文摘要：
The Barnich--Troessaert bracket is a proposal for a modified Poisson bracket on the covariant phase space for general relativity. The new bracket allows us to compute charges, which are otherwise not integrable. Yet there is a catch. There is a clear prescription for how to evaluate the new bracket for any such charge, but little is known how to extend the bracket to the entire phase space. This is a problem, because not every gravitational observable is also a charge. In this paper, we propose such an extension. The basic idea is to remove the radiative data from the covariant phase space. This requires second-class constraints. Given a few basic assumptions, we show that the resulting Dirac bracket on the constraint surface is nothing but the BT bracket. A heuristic argument is given to show that the resulting constraint surface can only contain gravitational edge modes.
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。
