  In this paper we propose an algebraic formulation of group field theory and
consider non-Fock representations based on coherent states. We show that we can
construct representations with infinite number of degrees of freedom on compact
base manifolds. We also show that these representations break translation
symmetry. Since such representations can be regarded as quantum gravitational
systems with an infinite number of fundamental pre-geometric building blocks,
they may be more suitable for the description of effective geometrical phases
of the theory.
