  We introduce a new loop expansion that provides a resolution of the identity
in the Hilbert space of loop quantum gravity on a fixed graph. We work in the
bosonic representation obtained by the canonical quantization of the spinorial
formalism. The resolution of the identity gives a tool for implementing the
projection of states in the full bosonic representation onto the space of
solutions to the Gauss and area matching constraints of loop quantum gravity.
This procedure is particularly efficient in the semiclassical regime, leading
to explicit expressions for the loop expansions of coherent, heat kernel and
squeezed states.
