Gravitons in loop quantum gravity

Recently, Ashtekar, Rovelli and Smolin developed a loop representation for linearized quantum general relativity. They succeeded in deriving the Fock space structure for gravitons, based on loop functionals. In this article we study the relation of this theory to the full loop representation for quantum general relativity of Rovelli and Smolin. We show, after having reformulated the full loop representation by defining it on loop triplets, how the graviton loop states can be embedded in it. Also we investigate which operators on the full theory and operators on the graviton states correspond to each other. An explicit linear embedding is constructed, mapping states and operators of full- and linearized theory into another. This embedding helps us in interpreting states and operators of loop quantum general relativity.