Chern--Simons states in spin-network quantum gravity

Details Chern--Simons states in spin-network quantum gravity Chern--Simons states in spin-network quantum gravity

1997-03-17

arxiv.org/abs/gr-qc/9703042v1

Phys.Lett. B413 (1997) 260-266

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, RevTeX, 17 figures included

Scientific paper

10.1016/S0370-2693(97)01048-4

In the context of canonical quantum gravity in terms of Ashtekar's new variables, it is known that there exists a state that is annihilated by all the quantum constraints and that is given by the exponential of the Chern--Simons form constructed with the Asthekar connection. We make a first exploration of the transform of this state into the spin-network representation of quantum gravity. The discussion is limited to trivalent nets with planar intersections. We adapt an invariant of tangles to construct the transform and study the action of the Hamiltonian constraint on it. We show that the first two coefficients of the expansion of the invariant in terms of the inverse cosmological constant are annihilated by the Hamiltonian constraint. We also discuss issues of framing that arise in the construction.

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