  We show that loop gravity can equally well be formulated in in terms of
spinorial variables (instead of the group variables which are commonly used),
which have recently been shown to provide a direct link between spin network
states and discrete geometries. This results in a new, unitarily equivalent
formulation of the theory on a generalized Bargmann space. Since integrals over
the group are exchanged for straightforward integrals over the complex plane we
expect this formalism to be useful to efficiently organize practical
calculations.
