Quantum deformation of quantum gravity

Details Quantum deformation of quantum gravity Quantum deformation of quantum gravity

1995-12-09

arxiv.org/abs/gr-qc/9512020v1

Nucl.Phys.B473:267-290,1996

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, many figures

Scientific paper

10.1016/0550-3213(96)00259-3

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 deformation parameter, q, depends on the cosmological constant. The Mandelstam 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. Corrections to the actions of operators in non-perturbative 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 q-deformed connection representation through an inverse transform.

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