Frozen formalism and canonical quantization in group field theory

Canonical quantization of gravitational systems is obstructed by the problem time. Due to diffeomorphism symmetry Hamiltonian vanishes: dynamics with respect a background time parameter appears "frozen." Two strategies towards such are identification clock degree freedom before (deparametrization), and on kinematical Hilbert space which subject constraints (Dirac quantization). The usual canonical in quantum field theory analogous deparametrization. Here we introduce frozen formalism Dirac for complex Klein-Gordon scalar field, show that resulting equivalent quantization. We then apply group gravity, both deparametrization "timeless" have been proposed past work. how links between these two existing approaches, illustrate particular construction physical observables. derive effective cosmological new compare previous could be extended other approaches gravity do not use preferred parameter.