The geometry of quantum spin networks

Type of Work

Article

Date

1996

Journal Title

Classical and Quantum Gravity

Journal ISSN

0264-9381

Journal Volume

13

Journal Issue

12

First Page

3183

Last Page

3196

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 of the observable algebra. Operators for area and volume are extended to this theory and, 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 , which simplifies the construction of these and other operators through diffeomorphism invariant regularization procedures.

Hamilton Areas of Study

Physics

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