SPIN NETWORKS AND QUANTUM-GRAVITY

We introduce a new basis on the state space of nonperturbative quantum gravity. The states of this basis are linearly independent, are well defined in both the loop representation and the connection representat ion, and are labeled by a generalisation of Penrose's spin networks. T he new basis fully reduces the spinor identities [SU(2) Mandelstam ide ntities] and simplifies calculations in nonperturbative quantum gravit y. In particular, it allows a simple expression for the: exact solutio ns of the Hamiltonian constraint (Wheeler-DeWitt equation) that have b een discovered in the loop representation. The states in this basis di agonalize operators that represent the three-geometry of space, such a s the area and the volume of arbitrary surfaces and regions, and there fore provide a discrete picture of quantum geometry at the Planck scal e.