论文标题
球形对称性超表面变形中的Abelianizatized结构
Abelianized structures in spherically symmetric hypersurface deformations
论文作者
论文摘要
在规范的重力中，一般的协方差是通过相位空间上的超表面性对称性实现的。完全协方差所需的不同版本的超表面变形具有复杂的相互作用，并由具有结构函数的非亚伯式支架约束。对于球形对称的空间时间，可以在一般超出表面变形中识别某些ABELIAN子结构，这表明简化的实现为Lie代数。该子结构的发电机可以比完整的Hyperface变形更容易量化，但是它们生成的对称性并不直接对应于HyperSurface变形。因此，一致量化的可用性不能保证一般的协方差或有意义的量子概念。除了将Abelian子结构放在球形对称超出表面变形的整个上下文中，本文还指出了与量化时空结构中未遂应用相关的几个细微之处。特别是，因此，甘比尼，奥尔德多和普林在阿贝里亚化环境中的最新建筑无法解决环路量子重力的协方差危机。
In canonical gravity, general covariance is implemented by hypersurface-deformation symmetries on phase space. The different versions of hypersurface deformations required for full covariance have complicated interplays with one another, governed by non-Abelian brackets with structure functions. For spherically symmetric space-times, it is possible to identify a certain Abelian substructure within general hypersurface deformations, which suggests a simplified realization as a Lie algebra. The generators of this substructure can be quantized more easily than full hypersurface deformations, but the symmetries they generate do not directly correspond to hypersurface deformations. The availability of consistent quantizations therefore does not guarantee general covariance or a meaningful quantum notion thereof. In addition to placing the Abelian substructure within the full context of spherically symmetric hypersurface deformation, this paper points out several subtleties relevant for attempted applications in quantized space-time structures. In particular, it follows that recent constructions by Gambini, Olmedo and Pullin in an Abelianized setting fail to address the covariance crisis of loop quantum gravity.
