离散量子引力：II。状态和模型中的单纯复形、SL（2，C）的不表示和Lorentz不变权
Discrete Quantum Gravity: II. Simplicial complexes, irreps of SL(2,C), and a Lorentz invariant weight in a state sum model
摘要：
在[1]的第一部分中，我们发展了SO（4）的张量和自旋表示，以便将其应用于Barrett-Crane模型的单纯分解。我们附加到三角形的每个面的球函数构造的Dolginov-Biedenharn功能。在第二部分中，我们将同样的技术应用于洛伦兹不变状态和模型。我们需要三种新的成分：在单纯分解中出现的边和相应子空间的分类，SL（2，C）的不表示及其与出现在4-单纯形中的双向量的同构，单纯分解面上的单纯表示需要由张量积的交织条件得到的带状球函数。
英文摘要：
In part I of [1] we have developed the tensor and spin representation of SO(4) in order to apply it to the simplicial decomposition of the Barrett-Crane model. We attach to each face of a triangle the spherical function constructed from the Dolginov-Biedenharn function. In part II we apply the same technique to the Lorentz invariant state sum model. We need three new ingredients: the classification of the edges and the corresponding subspaces that arises in the simplicial decomposition, the irreps of SL(2,C) and its isomorphism to the bivectors appearing in the 4-simplices, the need of a zonal spherical function from the intertwining condition of the tensor product for the simple representations attached to the faces of the simplicial decomposition.
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