THE GEOMETRY OF QUANTUM SPIN NETWORKS

The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation of the obs ervable algebra. Operators for area and volume are extended to this th eory and, partly, diagonalized. The eigenstates are expressed in terms of q-deformed spin networks. The q-deformation breaks some of the deg eneracy of the volume operator so that trivalent spin networks have no n-zero volume. These computations are facilitated by use of a techniqu e based on the recoupling theory of SU(2)(q), which simplifies the con struction of these and other operators through diffeomorphism invarian t regularization procedures.