  Loop quantum gravity (LQG) is a quantization program for gravity based on the
principles of QFT and general covariance of general relativity. Quantum states
of LQG describe gravitational excitations based on graphs embedded in a spatial
slice of spacetime. We show that, under certain assumptions on the class of
diffeomorphisms, the space of diffeomorphism invariant states carries a Fock
space structure. The role of one-particle excitations for this structure is
played by the diffeomorphism invariant states based on graphs with a single
(linked) component. This means, however, that a lot of the structure of the
diffeomorphism invariant Hilbert space remains unresolved by this structure. We
show how the Fock structure allows to write at least some condensate states of
group field theory as diffeomorphism invariant coherent states of LQG in a
precise sense. We also show how to construct other interesting states using
this Fock structure. We finally explore the quantum geometry of single- and
multi-particle states and tentatively observe some resemblance to geometries
with a single or multiple components, respectively.
