Quantum gravity Hamiltonian for manifolds with boundary.

In canonical quantum gravity, when space is a compact manifold with boundary there is a Hamiltonian given by an integral over the boundary. Here we compute the action of this `boundary Hamiltonian' on observables corresponding to open Wilson lines in the new variables formulation of quantum gravity. Up to a divergent factor, it is given by a `shift operator' resembling that in Morales-T ecotl and Rovelli's work on quantum gravity coupled to Weyl spinors. This suggests the appearance of spinorial degrees of freedom on the boundary.