三维欧氏引力的组合量子化
Combinatorial quantisation of Euclidean gravity in three dimensions
摘要：
在2+1维爱因斯坦引力的Chern-Simons表述中，引力的相空间是平坦G-联络的模空间，其中G是典型的非紧李群，它依赖于时空的特征和宇宙学常数。对于欧几里得签名和消失的宇宙学常数，G是三维欧几里得群。对于这种情况下的泊松结构的模空间明确给出了一个经典的r-矩阵。它表明，量子双D（SU（2））的量子R-矩阵提供了一个量子化的泊松结构。
英文摘要：
In the Chern-Simons formulation of Einstein gravity in 2+1 dimensions the phase space of gravity is the moduli space of flat G-connections, where G is a typically non-compact Lie group which depends on the signature of space-time and the cosmological constant. For Euclidean signature and vanishing cosmological constant, G is the three-dimensional Euclidean group. For this case the Poisson structure of the moduli space is given explicitly in terms of a classical r-matrix. It is shown that the quantum R-matrix of the quantum double D(SU(2)) provides a quantisation of that Poisson structure.
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