On knottings in the physical Hilbert space of LQG as given by the EPRL model
On knottings in the physical Hilbert space of LQG as given by the EPRL model
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关于 EPRL 模型给出的 LQG 物理希尔伯特空间中的结
DOI：
10.1088/0264-9381/28/4/045002
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发表时间：
2010
影响因子：
3.5
通讯作者：
Benjamin Bahr
中科院分区：
文献类型：
--
作者：
Benjamin Bahr
我们考虑任意嵌入两个复合物的EPRL自旋泡沫振幅。选择的定义的脸和边缘的振幅，导致自旋泡沫振幅不变下平凡的细分，我们调查一致的变形下的振幅的不变性，这是嵌入式的两个复杂的变形，其中面被允许通过彼此在一个控制的方式。利用这个令人惊讶的不变性，我们能够证明物理希尔伯特空间，由所有自旋泡沫的总和定义，不再包含关于打结类的信息。
We consider the EPRL spin foam amplitude for arbitrary embedded two-complexes. Choosing a definition of the face- and edge amplitudes which lead to spin foam amplitudes invariant under trivial subdivisions, we investigate invariance properties of the amplitude under consistent deformations, which are deformations of the embedded two-complex where faces are allowed to pass through each other in a controlled way. Using this surprising invariance, we are able to show that the physical Hilbert space, as defined by the sum over all spin foams, contains no information about knotting classes of graphs anymore.