  We continue here the analysis of the previous paper of the Wheeler-DeWitt
constraint operator for four-dimensional, Lorentzian, non-perturbative,
canonical vacuum quantum gravity in the continuum. In this paper we derive the
complete kernel, as well as a physical inner product on it, for a non-symmetric
version of the Wheeler-DeWitt operator. We then define a symmetric version of
the Wheeler-DeWitt operator. For the Euclidean Wheeler-DeWitt operator as well
as for the generator of the Wick transform from the Euclidean to the Lorentzian
regime we prove existence of self-adjoint extensions and based on these we
present a method of proof of self-adjoint extensions for the Lorentzian
operator. Finally we comment on the status of the Wick rotation transform in
the light of the present results.
