QUANTUM DEFORMATION OF QUANTUM-GRAVITY

We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for descri bing a phase of quantum gravity characterized by states which are norm alizable in the measure of Chem-Simons theory. The spinor identities a re extended to a set of relations which are governed by the Kauffman b racket so that the spin network basis is deformed to a basis of SU(2)( q) spin networks, This deformation parameter, q, is e(iHBAR2G2 Lambda/ 6), where Lambda is the cosmological constant. Corrections to the acti ons of operators in nonperturbative quantum gravity may be readily com puted using recoupling theory; the example of the area observable is t reated here. Finally, eigenstates of the q-deformed Wilson loops are c onstructed, which may make possible the construction of a q-deformed c onnection representation through an inverse transform.