相空间约化的量子几何
Quantum geometry from phase space reduction
摘要：
本文给出了通常的自旋网络基与四面体约化相空间的直接量子化之间的显式同构。主要结果是一个公式，它描述了空间的SU（2）不变态的积分满足封闭约束的相干态，完全或等价地，作为一个积分的空间的经典四面体。这提供了一个明确的实现定理Guillemin-Sternberg和霍尔描述的交换的量化和减少。在文章的最后部分，我们利用我们的结果将FK自旋泡沫模型表示为经典四面体上的积分，并确定了顶点振幅的渐近性。
英文摘要：
In this work we give an explicit isomorphism between the usual spin network basis and the direct quantization of the reduced phase space of tetrahedra. The main outcome is a formula that describes the space of SU(2) invariant states by an integral over coherent states satisfying the closure constraint exactly, or equivalently, as an integral over the space of classical tetrahedra. This provides an explicit realization of theorems by Guillemin--Sternberg and Hall that describe the commutation of quantization and reduction. In the final part of the paper, we use our result to express the FK spin foam model as an integral over classical tetrahedra and the asymptotics of the vertex amplitude is determined.
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