On the quantization of the linearized gravitational field

We present a new point of view on the quantization of the gravitational field, namely we use exclusively the quantum framework of the second quantization. More explicitly, we take as one-particle Hilbert space, H-graviton the unitary irreducible representation of the Poincare group corresponding to a massless particle of helicity 2 and apply the second quantization procedure with Einstein-Bose statistics. The resulting Hilbert space F+(H-graviton) is, by definition, the Hilbert space of the gravitational field. Then we prove that this Hilbert space is canonically isomorphic to a space of the type Ker(Q)/Im(Q) where Q is a supercharge defined in an extension of the Hilbert space F+(H-graviton) by the inclusion of ghosts: some fermion ghosts u(mu), (u)over tilde>(mu) which are vector fields and a bosonic ghost Phi which is a scalar field. This has to be contrasted with the usual approaches where only the fermion ghosts are considered. However, a rigorous proof that this is, indeed, possible seems to be lacking in the literature.