U(N) tools for loop quantum gravity: the return of the spinor
U(N) tools for loop quantum gravity: the return of the spinor
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圈量子引力的 U(N) 工具：旋量的返回
DOI：
10.1088/0264-9381/28/5/055005
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发表时间：
2010
影响因子：
3.5
通讯作者：
E. Livine
中科院分区：
文献类型：
--
作者：
Enrique F. Borja;L. Freidel;Iñaki Garay;E. Livine
我们探索了SU(2)环路量子引力交织体U(N)框架的经典设置，并在适当的约束下用旋量描述了相应的相空间。我们展示了它的量子化如何回到定义为全纯泛函的交织状态的标准希尔伯特空间。然后，我们解释了如何粘合这些缠绕在一起的态，以便在旋量相空间上将自旋网络态构造为波函数。特别是，我们将通常的回路引力完整观测值转换到我们的经典框架中。最后，我们提出了如何从一个导致自旋网络态的非平凡动力学的作用原理来推导我们的相空间结构。最后，我们显式地将我们的框架应用于简单的2-顶点图上的状态，并讨论了由此产生的哈密顿量的性质。
We explore the classical setting for the U(N) framework for SU(2) intertwiners for loop quantum gravity and describe the corresponding phase space in terms of spinors with the appropriate constraints. We show how its quantization leads back to the standard Hilbert space of intertwiner states defined as holomorphic functionals. We then explain how to glue these intertwiners states in order to construct spin network states as wavefunctions on the spinor phase space. In particular, we translate the usual loop gravity holonomy observables to our classical framework. Finally, we propose how to derive our phase space structure from an action principle which induces non-trivial dynamics for the spin network states. We conclude by applying explicitly our framework to states living on the simple 2-vertex graph and discuss the properties of the resulting Hamiltonian.