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 describing a phase of quantum gravity characterized by states which are normalizable in the measure of Chern-Simons theory. The spinor identities are extended to a set of relations which are governed by the Kauffman bracket so that the spin network basis is deformed to a basis of SU(2)q spin networks. This deformation parameter, q, is eih̵2G2Λ6 role= presentation style= box-sizing: border-box; display: inline-block; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(80, 80, 80); font-family: Arial, Helvetica, Lucida Sans Unicode , Microsoft Sans Serif , Segoe UI Symbol , STIXGeneral, Cambria Math , Arial Unicode MS , sans-serif; position: relative; \u3e̵eih̵2G2Λ6, where Λ is the cosmological constant. Corrections to the actions of operators in nonperturbative quantum gravity may be readily computed using recoupling theory; the example of the area observable is treated here. Finally, eigenstates of the q-deformed Wilson loops are constructed, which may make possible the construction of a -deformed connection representation through an inverse transform