SU(2)-INVARIANT REDUCTION OF (3-DIMENSIONAL ASHTEKAR GRAVITY(1))

We consider a spacetime with spatial sections isomorphic to the group manifold of SU(2). Triad and connection fluctuations are assumed to be SU(2) invariant. Thus they form a finite-dimensional phase space. We perform non-perturbative path-integral quantization of the model. Cont rary to previous claims, the path integral measure appeared to be non- singular near configurations admitting additional Killing vectors. In this model we are able to calculate the generating functional of Green functions of the reduced phase space variables exactly.