  Exact solutions of the Wheeler-DeWitt equation of the full theory of four
dimensional gravity of Lorentzian signature are obtained. They are
characterized by Schr\"odinger wavefunctionals having support on 3-metrics of
constant spatial scalar curvature, and thus contain two full physical field
degrees of freedom in accordance with the Yamabe construction. These solutions
are moreover Gaussians of minimum uncertainty and they are naturally associated
with a rigged Hilbert space. In addition, in the limit the regulator is
removed, exact 3-dimensional diffeomorphism and local gauge invariance of the
solutions are recovered.
