The geometry of quantum spin networks
arXiv:gr-qc/9512043 · doi:10.1088/0264-9381/13/12/009
Abstract
The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation. The operators for area and volume defined in the q-deformation of the theory are partly diagonalized. The eigenstates are expressed in terms of q-deformed spin networks. The q-deformation breaks some of the degeneracy of the volume operator so that trivalent spin-networks have non-zero volume. These computations are facilitated by use of a technique based on the recoupling theory of SU(2)_q, which simplifies the construction of these and other operators through diffeomorphism invariant regularization procedures.
16 pages, 35 Postscript figures, uses epsfig.sty
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