  Group field theory posits that spacetime is emergent and is hence defined
without any background notion of space or time; dynamical questions are
formulated in relational terms, in particular using (scalar) matter degrees of
freedom as time. Unlike in canonical quantisation of gravitational systems,
there is no obvious notion of coordinate transformations or constraints, and
established quantisation methods cannot be directly applied. As a result,
different canonical formalisms for group field theory have been discussed in
the literature. We address these issues using a parametrised version of group
field theory, in which all (geometry and matter) degrees of freedom evolve in a
fiducial parameter. There is a constraint associated to the freedom of
reparametrisation and the Dirac quantisation programme can be implemented.
Using the "trinity of relational dynamics", we show that the resulting
"clock-neutral" theory is entirely equivalent to a deparametrised canonical
group field theory, interpreted in terms of the Page-Wootters formalism. Our
results not only show that the deparametrised quantisation is fully covariant
and can be seen as encoding the dynamics of joint quantum matter and geometry
degrees of freedom, they also appear to be the first application of the
Page-Wootters formalism directly to non-perturbative quantum gravity. We show
extensions to a setting in which many independent gauge symmetries are
introduced, which connects to the "multi-fingered time" idea in quantum gravity
and provides a somewhat novel extension of the Page-Wootters formalism.
