An Introduction to spin foam models of quantum gravity and BF theory
An Introduction to spin foam models of quantum gravity and BF theory
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DOI：
10.1007/3-540-46552-9_2
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发表时间：
1999-05
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影响因子：
--
通讯作者：
J. Baez
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文献类型：
--
作者：
J. Baez
在环形量子引力中，我们现在对空间的量子几何有了清晰的了解，这在一定程度上要归功于自旋网络理论。“自旋泡沫”的概念旨在为时空的量子几何学提供类似的图景。一般说来，自旋网络是一个图，它的边用表示标记，顶点用缠绕算子标记。类似地，自旋泡沫是一个2维复合体，其中面由表示标记，边由缠绕操作符标记。在“自旋泡沫模型”中，我们将状态描述为自旋网络的线性组合，并将跃迁幅度计算为自旋泡沫的总和。本文旨在提供一个完整的介绍量子引力的自旋泡沫模型和一个更简单的场论--BF理论。
In loop quantum gravity we now have a clear picture of the quantum geometry ofspace, thanks in part to the theory of spin networks. The concept of ‘spin foam’ is intended to serve as a similar picture for the quantum geometry ofspacetime. In general, a spin network is a graph with edges labeled by represen- tations and vertices labeled by intertwining operators. Similarly, a spin foam is a 2-dimensional complex with faces labeled by representations and edges labeled by intertwining operators. In a ‘spin foam model’ we describe states as linear combina- tions of spin networks and compute transition amplitudes as sums over spin foams. This paper aims to provide a self-contained introduction to spin foam models of quantum gravity and a simpler field theory calledBFtheory.