Spin Networks and Recoupling in Loop Quantum Gravity

Details Spin Networks and Recoupling in Loop Quantum Gravity Spin Networks and Recoupling in Loop Quantum Gravity

1997-01-18

arxiv.org/abs/gr-qc/9701041v1

Nucl.Phys.Proc.Suppl. 57 (1997) 251-254

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, LaTeX3e, To appear in the Proceedings of the 2nd Conference on Constrained Dynamics and Quantum Gravity, Santa Marghe

Scientific paper

10.1016/S0920-5632(97)00397-6

I discuss the role played by the spin-network basis and recoupling theory (in its graphical tangle-theoretic formulation) and their use for performing explicit calculations in loop quantum gravity. In particular, I show that recoupling theory allows the derivation of explicit expressions for the eingenvalues of the quantum volume operator. An important side result of these computations is the determination of a scalar product with respect to which area and volume operators are symmetric, and the spin network states are orthonormal.

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