  The Hamiltonian reduction of the massless spin-two field theory is carried
out following the Faddeev-Jackiw approach. The reduced Hamiltonian contains
only the traceless-transverse fields, but not all of the non-propagating
components can be determined by the constraints of the theory. The reason for
this is found in the fact that the Hamiltonian is not gauge invariant.
Consequences and implications for General Relativity are discussed and
illustrated on the example of Robertson-Walker cosmologies with a scalar field.
Also, it it shown that for those explicitely solvable models, the reduced form
of the dynamics uniquely determines the operator ordering that has to be
adopted in the Wheeler-DeWitt equation in order to maintain consistency.
