SPIN NETWORKS AND RECOUPLING IN LOOP QUANTUM-GRAVITY

I discuss the role played by the spin-network basis and recoupling the ory (in its graphical tangle-theoretic formulation) and their use in p erforming explicit calculations in loop quantum gravity. In particular , I show that recoupling theory allows the derivation of explicit expr essions for the eigenvalues of the quantum volume operator. An importa nt 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 orthonormal.