论文标题
2+1维量子重力中的因果钻石
Causal diamonds in 2+1 dimensional quantum gravity
论文作者
论文摘要
我们发展了纯2+1维重力中因果钻石的相位空间量化，具有非阳性宇宙常数。该系统被定义为具有固定边界指标的拓扑盘的依赖性领域。通过在恒定均值的时间表中求解初始值约束并删除所有空间规冗余，我们发现相位空间是diff^+（s^1）/psl（2，r）的cotangangent束。为了量化此相空间，我们在BMS_3组方面应用了ISHAM的组理论量化方案，并发现量子理论可以通过Virasoro组的某些coadchoint轨道上的波函数实现，并在相应小组的不可约合的统一表示中标记。我们发现，钻石边界环的扭曲以整数或半数的倍数量化了普朗克长度与边界长度的比例。
We develop the reduced phase space quantization of causal diamonds in pure 2+1 dimensional gravity with a non-positive cosmological constant. The system is defined as the domain of dependence of a topological disc with fixed boundary metric. By solving the initial value constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of Diff^+(S^1)/PSL(2,R). To quantize this phase space we apply Isham's group-theoretic quantization scheme, with respect to a BMS_3 group, and find that the quantum theory can be realized by wavefunctions on some coadjoint orbit of the Virasoro group, with labels in irreducible unitary representations of the corresponding little group. We find that the twist of the diamond boundary loop is quantized in integer or half-integer multiples of the ratio of the Planck length to the boundary length.
