Quantum Gravity Vacuum and Invariants of Embedded Spin Networks

Details Quantum Gravity Vacuum and Invariants of Embedded Spin Networks Quantum Gravity Vacuum and Invariants of Embedded Spin Networks

2003-01-14

arxiv.org/abs/gr-qc/0301047v2

Class.Quant.Grav.20:3483-3492,2003

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, revised version to appear in Class. Quant. Grav

Scientific paper

10.1088/0264-9381/20/15/314

We show that the path integral for the three-dimensional SU(2) BF theory with a Wilson loop or a spin network function inserted can be understood as the Rovelli-Smolin loop transform of a wavefunction in the Ashtekar connection representation, where the wavefunction satisfies the constraints of quantum general relativity with zero cosmological constant. This wavefunction is given as a product of the delta functions of the SU(2) field strength and therefore it can be naturally associated to a flat connection spacetime. The loop transform can be defined rigorously via the quantum SU(2) group, as a spin foam state sum model, so that one obtains invariants of spin networks embedded in a three-manifold. These invariants define a flat connection vacuum state in the q-deformed spin network basis. We then propose a modification of this construction in order to obtain a vacuum state corresponding to the flat metric spacetime.

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