  We show that the Hamiltonian of four-dimensional Lorentzian gravity, defined
on a space of real, SU(2)-valued connections, in spite of its non-polynomiality
possesses a natural quantum analogue in a lattice-discretized formulation of
the theory. This opens the way for a systematic investigation of its spectrum.
The unambiguous and well-defined scalar product is that of the SU(2)-gauge
theory. We also comment on various aspects of the continuum theory.
