论文标题
可集成重力电荷的模棱两可的分辨率
Ambiguity resolution for integrable gravitational charges
论文作者
论文摘要
最近，Ciambelli，Leigh和Pai（CLP）[ARXIV：2111.13181]表明，可以定义集成汉密尔顿方程的非零电荷，用于在重力理论中属于子区域边界的所有差异性。这是通过将相位空间扩展到包含一组嵌入字段来完成的，以参数化边界的位置。由于它们的构造与以前在扩展相位空间上通过协变相空间歧义的不同之处，因此出现了关于结果是否明确定义的问题。在这里，我们证明了无歧义的费用可以通过吸引子区域的各种原则来获得无歧义的费用，这是在处理协方差阶段空间中边界的最新发展之后。解决歧义会产生校正差异性电荷，还会对汉密尔顿方程的可集成性产生额外的障碍。我们强调了一个事实，即CLP扩展的相空间会产生非零的差异性电荷与以前的结构区分开，在这种结构中，差异性是纯仪表，因为始终可以通过选择单位量规来从后者中消除嵌入的场。最后，我们表明，Wald-Zoupas电荷具有对可集成性的特征性障碍，与扩展相空间中的改进转换有关，阐明了汉密尔顿方程在标准差异性方程的集成性背后的原因。
Recently, Ciambelli, Leigh, and Pai (CLP) [arXiv:2111.13181] have shown that nonzero charges integrating Hamilton's equation can be defined for all diffeomorphisms acting near the boundary of a subregion in a gravitational theory. This is done by extending the phase space to include a set of embedding fields that parameterize the location of the boundary. Because their construction differs from previous works on extended phase spaces by a covariant phase space ambiguity, the question arises as to whether the resulting charges are unambiguously defined. Here, we demonstrate that ambiguity-free charges can be obtained by appealing to the variational principle for the subregion, following recent developments on dealing with boundaries in the covariant phase space. Resolving the ambiguity produces corrections to the diffeomorphism charges, and also generates additional obstructions to integrability of Hamilton's equation. We emphasize the fact that the CLP extended phase space produces nonzero diffeomorphism charges distinguishes it from previous constructions in which diffeomorphisms are pure gauge, since the embedding fields can always be eliminated from the latter by a choice of unitary gauge. Finally, we show that Wald-Zoupas charges, with their characteristic obstruction to integrability, are associated with a modified transformation in the extended phase space, clarifying the reason behind integrability of Hamilton's equation for standard diffeomorphisms.
