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

Autor:	Kramer, P., Lorente, M.
Rok vydání:	2008
Předmět:	General Relativity and Quantum Cosmology
Druh dokumentu:	Working Paper
Popis:	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. Comment: LaTex 19 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0804.4162 Zobrazit plný text záznamu View this record from Arxiv