Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-04-25
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
LaTex 19 pages
Scientific paper
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.
Kramer Peter
Lorente Miguel
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