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Abstract

We perform a canonical quantization of Weyl's conformal gravity by means of
the covariant operator formalism and investigate the unitarity of the resulting
quantum theory. After reducing the originally fourth order theory to second
order in time derivatives via the introduction of an auxiliary tensor field, we
identify the full Fock space of quantum states under a BRST construction that
includes Faddeev-Popov ghost fields corresponding to Weyl transformations.
Using the Kugo-Ojima quartet mechanism, we identify the physical subspace of
quantum states and find that the subspace containing the transverse spin-2
states comes equipped with an indefinite inner product metric and a
one-particle Hamiltonian that possesses only a single eigenstate. We construct
the LSZ reduction formula for the S-matrix in this spin-2 subspace and find
that unitarity is violated in scattering events. The explicit way in which this
violation occurs represents a new view on the ghost-problem in quadratic
theories of quantum gravity.