Tensor and spin representations of SO(4) and discrete quantum gravity

Details Tensor and spin representations of SO(4) and discrete quantum gravity Tensor and spin representations of SO(4) and discrete quantum gravity

2004-02-11

arxiv.org/abs/gr-qc/0402050v4

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 18 pages, 1 eps figure. Communication presented to the International Symposium Symmetries in Science XIII, July 2003, B

Scientific paper

Starting from the defining transformations of complex matrices for the SO(4) group, we construct the fundamental representation and the tensor and spinor representations of the group SO(4). Given the commutation relations for the corresponding algebra, the unitary representations of the group in terms of the generalized Euler angles are constructed. These mathematical results help us to a more complete description of the Barrett-Crane model in Quantum Gravity. In particular a complete realization of the weight function for the partition function is given and a new geometrical itnerpretation of the asymptotic limit for the Regge action is presented.

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