  We achieve a group theoretical quantization of the flat
Friedmann-Robertson-Walker model coupled to a massless scalar field adopting
the improved dynamics of loop quantum cosmology. Deparemeterizing the system
using the scalar field as internal time, we first identify a complete set of
phase space observables whose Poisson algebra is isomorphic to the su(1,1) Lie
algebra. It is generated by the volume observable and the Hamiltonian. These
observables describe faithfully the regularized phase space underlying the loop
quantization: they account for the polymerization of the variable conjugate to
the volume and for the existence of a kinematical non-vanishing minimum volume.
Since the Hamiltonian is an element in the su(1,1) Lie algebra, the dynamics is
now implemented as SU(1,1) transformations. At the quantum level, the system is
quantized as a time-like irreducible representation of the group SU(1,1). These
representations are labeled by a half-integer spin, which gives the minimal
volume. They provide superselection sectors without quantization anomalies and
no factor ordering ambiguity arises when representing the Hamiltonian. We then
explicitly construct SU(1,1) coherent states to study the quantum evolution.
They not only provide semiclassical states but truly dynamical coherent states.
Their use further clarifies the nature of the bounce that resolves the big bang
singularity.
