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arXiv · 0804.4162

Discrete Quantum Gravity: II. Simplicial complexes, irreps of SL(2,C), and a Lorentz invariant weight in a state sum model

P. Kramer·M. Lorente
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Abstract

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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P. Kramer, M. Lorente. 2008-04-30. Discrete Quantum Gravity: II. Simplicial complexes, irreps of SL(2,C), and a Lorentz invariant weight in a state sum model. https://arxiv.org/abs/0804.4162

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