Hamiltonian reduction of spin-two theory and of solvable cosmologies

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.