  In this paper we have carried out a transformation from Ashtekar's theory of
GR into a reduced theory where the physical degrees of freedom are explicit. We
have performed the canonical analysis, computed the classical dynamics and have
performed a quantization on this reduced space, constructing a Hilbert space of
states for vanishing cosmological constant. Finally, we have clarified the
canonical structure of the dual theory in relation to the original Ashtekar
theory.
