  One can simplify the triad formulations of canonical gravity by abandoning
any relation to a fixed coordinate system. That means in case of the \ADM
formalism that one can determine the momentum by direct derivation of the
Lagrange-3-form w.r.t the time-derivative of the triad-1-forms, thus the
momentum is most naturally a 2-form. We apply this concept to the Palatini
formulation where we can closely follow Dirac's concept to find and eliminate
the second class constraints. Following the same way for the Ashtekar theory it
will turn out to be equivalent to two successive canonical transformations
where the first makes explicit use of the spatial dimension being 3 and the
second is usually hidden in the use of densities. At the end we can give a
simple version of the reality constraints.
