  Quantum gravity is extended to include purely virtual "cloud sectors", which
allow us to define a complete set of point-dependent observables, including a
gauge invariant metric and gauge invariant matter fields, and calculate their
off-shell correlation functions perturbatively. The ordinary on-shell
correlation functions and the $S$ matrix elements are unaffected. Each extra
sector is made of a cloud field, its anticommuting partner, a "cloud-fixing"
function and a cloud Faddeev-Popov determinant. The additional fields are
purely virtual, to ensure that no ghosts propagate. The extension is unitary.
In particular, the off-shell, diagrammatic version of the optical theorem
holds. The one-loop two-point functions of dressed scalars, vectors and
gravitons are calculated. Their absorptive parts are positive, cloud
independent and gauge independent, while they are unphysical if non purely
virtual clouds are used. We illustrate the differences between our approach to
the problem of finding a complete set of observables in quantum gravity and
other approaches available in the literature.
