A systematic derivation of the Riemannian Barrett-Crane intertwiner. (English) Zbl 1111.83020
Summary: The Barrett-Crane intertwiner for the Riemannian general relativity is systematically derived by solving the quantum Barrett-Crane constraints corresponding to a tetrahedron (except for the nondegeneracy condition). It was shown by Reisenberger that the Barrett-Crane intertwiner is the unique solution. The systematic derivation can be considered as an alternative proof of the uniqueness. The new element in the derivation is the rigorous imposition of the cross-simplicity constraint.
MSC:
| 83C45 | Quantization of the gravitational field |
| 81V17 | Gravitational interaction in quantum theory |
| 83C27 | Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory |
References:
| [1] | DOI: 10.1063/1.532254 · Zbl 0967.83006 · doi:10.1063/1.532254 |
| [2] | DOI: 10.1063/1.532850 · Zbl 0959.83020 · doi:10.1063/1.532850 |
| [3] | DOI: 10.4310/ATMP.1999.v3.n5.a3 · Zbl 0997.83020 · doi:10.4310/ATMP.1999.v3.n5.a3 |
| [4] | DOI: 10.1142/0270 · doi:10.1142/0270 |
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