The geometry of quantum spin networks

Details The geometry of quantum spin networks The geometry of quantum spin networks

1995-12-27

arxiv.org/abs/gr-qc/9512043v1

Class.Quant.Grav. 13 (1996) 3183-3196

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, 35 Postscript figures, uses epsfig.sty

Scientific paper

10.1088/0264-9381/13/12/009

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.

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