费曼图
Presently, no semiclassical limit recovering general relativity has been shown to exist. This means it remains unproven that LQGs description of spacetime at the Planck scale has the right continuum limit (described by general relativity with possible quantum corrections). Specifically, the dynamics of the theory are encoded in the Hamiltonian constraint, but there is no candidate Hamiltonian. Other technical problems include finding off-shell closure of the constraint algebra and physical inner product vector space, coupling to matter fields of quantum field theory, fate of the renormalization of the graviton in perturbation theory that lead to ultraviolet divergence beyond 2-loops (see one-loop Feynman diagram in Feynman diagram).