SU(2)-invariant reduction of (3+1)-dimensional Ashtekar gravity

Abstract

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. Contrary 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.