Spin Networks in Nonperturbative Quantum Gravity
Spin Networks in Nonperturbative Quantum Gravity
复制标题
非微扰量子引力中的自旋网络
DOI：
10.1090/psapm/051/1372769
复制
发表时间：
1995
期刊：
影响因子：
--
通讯作者：
J. Baez
中科院分区：
文献类型：
--
作者：
J. Baez
自旋网络是结或链接的概括：嵌入空间中的图，其边由李群的表示标记，顶点由交织算子标记。这些物体在 3 维拓扑量子场理论、连接模规范变换的空间 A=G 上的函数积分以及量子引力的循环表示中发挥着重要作用。在这里，在介绍了非微扰正则量子引力的基本思想之后，我们回顾了 A=G 上函数积分的严格方法，其中 L 2 (A=G) 由自旋网络标记的状态跨越。然后，我们解释 4 维时空中广义相对论的“新变量”，并描述这种形式主义中重力的正则量子化如何导致这些自旋网络状态的有趣应用。
A spin network is a generalization of a knot or link: a graph embedded in space, with edges labelled by representations of a Lie group, and vertices labelled by intertwining operators. Such objects play an important role in 3-dimensional topological quantum eld theory, functional integration on the spaceA=G of connections modulo gauge transformations, and the loop representation of quantum gravity. Here, after an introduction to the basic ideas of nonperturbative canonical quantum gravity, we review a rigorous approach to functional integration onA=G in which L 2 (A=G) is spanned by states labelled by spin networks. Then we explain the ‘new variables’ for general relativity in 4-dimensional spacetime and describe how canonical quantization of gravity in this formalism leads to interesting applications of these spin network states.