Gravitons from loops: non-perturbative loop-space quantum gravity contains the graviton-physics approximation

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We investigate the physical interpretation of the loop states of non-perturbative quantum general relativity in the regime of graviton physics, namely the regime of first order excitations around the Poincaré-invariant vacuum. We construct the general form of the loop state functionals invariant under the linearized constraints. We present explicitly the loop state functionals that represent the Poincaré-invariant vacuum and the graviton states. We find that physical information emerges entirely from intersections of loops. We obtain these results by utilizing the recently introduced `map ', which relates the loop-space states of non-perturbative quantum general relativity to the state space of the linearized theory. The general picture of the linearization of the loop-space quantum general relativity is discussed.