Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-04-25
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
LaTex 24 pages
Scientific paper
Starting from the defining transformations of complex matrices for the $SO(4,R)$ group, we construct the fundamental representation and the tensor and spinor representations of the group $SO(4,R)$. Given the commutation relations for the corresponding algebra, the unitary representations of the group in terms of the generalized Euler angles are constructed. The crucial step for the Barrett-Crane model in Quantum Gravity is the description of the amplitude for the quantum 4-simplex that is used in the state sum partition function. We obtain the zonal spherical functions for the construction of the SO(4,R) invariant weight and associate them to the triangular faces of the 4-simplices.
Kramer Peter
Lorente Miguel
No associations
LandOfFree
Discrete Quantum Gravity: I. Zonal spherical functions of the representationsof the SO(4,R) group with respect to the SU(2) subgroup and their application to the Barrett-Crane model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Discrete Quantum Gravity: I. Zonal spherical functions of the representationsof the SO(4,R) group with respect to the SU(2) subgroup and their application to the Barrett-Crane model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discrete Quantum Gravity: I. Zonal spherical functions of the representationsof the SO(4,R) group with respect to the SU(2) subgroup and their application to the Barrett-Crane model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-728221