Simplification of the constraints in the dirac formalism for general relativity

In any classical theory in canonical form, the Poisson bracket relations between the constraints are preserved under canonical transformations. We show that in the Dirac formalism for general relativity this condition places certain limits on the degree to which one can simplify the form of the constraints. It implies, for instance, that the constraints cannot all be written as canonical momenta. Furthermore, it is not even possible to reduce them all to purely algebraic functions of the momenta by means of a canonical tansformation which preserves the original configuration space subspace of phase space.