Gauge-invariant coherent states for loop quantum gravity: II. Non-Abelian gauge groups
Gauge-invariant coherent states for loop quantum gravity: II. Non-Abelian gauge groups
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圈量子引力的规范不变相干态：II。
DOI：
10.1088/0264-9381/26/4/045012
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发表时间：
2007
影响因子：
3.5
通讯作者：
T. Thiemann
中科院分区：
文献类型：
--
作者：
Benjamin Bahr;T. Thiemann
这是第二篇关于圈量子引力规范不变相干态的论文。在这里，我们处理规范群SU（2），这是一个显着的复杂性相比，阿贝尔U（1）的情况下遇到的前一篇文章（类。量子重力26 045011）。本文用解析和数值方法研究了某些特殊图上的规范不变相干态。我们发现，它们的重叠是高斯峰值规范不变量，只要状态不被标记的退化规范轨道，即点的规范不变的配置空间具有奇点。在这些情况下，重叠仍然集中在这些点周围，但峰形显示出平台结构。这表明了态的半经典性质如何受到规范不变相空间几何形状的影响。
This is the second paper concerning gauge-invariant coherent states for loop quantum gravity. Here, we deal with the gauge group SU(2), this being a significant complication compared to the Abelian U(1) case encountered in the previous article (Class. Quantum Grav. 26 045011). We study gauge-invariant coherent states on certain special graphs by analytical and numerical methods. We find that their overlap is Gauss peaked in gauge-invariant quantities, as long as states are not labeled by degenerate gauge orbits, i.e. points where the gauge-invariant configuration space has singularities. In these cases the overlaps are still concentrated around these points, but the peak profile exhibits a plateau structure. This shows how the semiclassical properties of the states are influenced by the geometry of the gauge-invariant phase space.