  The problem of time emerging in the canonical quantization procedure of
gravity signals a necessity to properly define a relational time parameter.
Previous approaches, which are here briefly discussed, make use of the
dependence of the quantum system on semiclassical gravitational variables in
order to define time. We show that such paths, despite the following studies,
lead to a non-unitary evolution. We propose a different model for the
quantization of the gravity-matter system, where the time parameter is defined
via an additional term, i.e. the kinematical action, which acts as a clock for
quantum matter. The procedure here used implements a Born-Oppenheimer-like
separation of the system, which maintains covariance under the foliation of the
gravitational background and keeps the correct classical limit of standard
quantum field theory on a fixed background. It is shown with a WKB expansion
that quantum gravity corrections to the matter dynamics arise at the next order
of expansion, and such contributions are unitary, signalling a striking
difference from previous proposals. Applications to a cosmological model are
presented and the analogies of the kinematical term with an incoherent dust are
briefly discussed.
