Spin Networks and Recoupling in Loop Quantum Gravity

Abstract

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.

8 pages, LaTeX3e, To appear in the Proceedings of the 2nd Conference on Constrained Dynamics and Quantum Gravity, Santa Margherita, Italy, 17-21 September 1996

References in corpus (4)

• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• Geometry Eigenvalues and Scalar Product from Recoupling Theory in Loop Quantum Gravity
• Volume and Quantizations
• On the relation between the connection and the loop representation of quantum gravity

Cited by in corpus (17)

• Background Independent Quantum Gravity: A Status Report
• Loop Quantum Cosmology
• Polyhedra in loop quantum gravity
• Simplification of the Spectral Analysis of the Volume Operator in Loop Quantum Gravity
• Spectral Analysis of the Volume Operator in Loop Quantum Gravity
• Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity I
• Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity II
• On (Cosmological) Singularity Avoidance in Loop Quantum Gravity
• Properties of the Volume Operator in Loop Quantum Gravity I: Results
• Properties of the Volume Operator in Loop Quantum Gravity II: Detailed Presentation
• Background independent quantizations: the scalar field II
• Modelling Space with an Atom of Quantum Geometry
• Bibliography of publications related to Classical and Quantum Gravity in terms of Connection and Loop Variables
• The Large-Volume Limit of a Quantum Tetrahedron is a Quantum Harmonic Oscillator
• Angle and Volume Studies in Quantized Space
• Classical and Quantum Polyhedra
• Properties of the Rovelli-Smolin-DePietri volume operator in the spaces of monochromatic intertwiners