CHERN-SIMONS STATES IN SPIN-NETWORK QUANTUM-GRAVITY

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 Chem-Simons form constructed with the Asthekar connection. We mak e a first exploration of the transform of this state into the spin-net work representation of quantum gravity. The discussion is limited to t rivalent nets with planar intersections. We adapt an invariant of tang les to construct the transform and study the action of the Hamiltonian constraint on it. We show that the first two coefficients of the expa nsion of the invariant in terms of the inverse cosmological constant a re annihilated by the Hamiltonian constraint. We also discuss issues o f framing that arise in the construction. (C) 1997 Elsevier Science B. V.