Faddeev-Jackiw quantization of spin-2 field

We apply the Faddeev-Jackiw method to the Hamiltonian analysis of the massless spin-two field. As expected, the reduced Hamiltonian contains only the traceless-transverse tensor, while some, but not all of the non-propagating components are determined by the constraints of the theory. In particular, it is concluded that no gauge choice can be imposed on the fields such that only the propagating modes remain in the theory, meaning that for the spin-2 field there is no direct analogue to the Coulomb gauge of electromagnetism. Implications for General Relativity are discussed.