1999/05/26 by Dan Radu Grigore · 1 citation
Physics and Astronomy · #hep-th
published as Class.Quant.Grav. 17 (2000) 319-344 · 32 pages, LATEX2E
arxiv created 1999/05/26 · arxiv updated 2009/11/30
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, Hgraviton the unitary irreducible representation of the Poincaré group corresponding to a massless particle of helicity 2 and apply the second quantization procedure with Einstein-Bose statistics. The resulting Hilbert space \cal F+(Hgraviton) 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 \cal F+ (Hgraviton) by the inclusion of ghosts: some Fermion ghosts uμ, uμ which are vector fields and a Bosonic ghost Φ which is a scalar field. This has to be contrasted to the usual approaches where only the Fermion ghosts are considered. However, a rigorous proof that this is, indeed, possible seems to be lacking from the literature.