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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. In cases where the boundary conditions fix the metric on the boundary (e.g., in the asymptotically Minkowskian case) one can obtain a finite result, given by a 'shift operator' generatingdoi:10.1103/physrevd.52.6840 pmid:10019223 fatcat:vsbkbycqhbb3dmgooypuq2ddma