In quantum gravity, summing is refining

Understand

In perturbative QED, the approximation is improved by summing more Feynman graphs; in non-perturbative QCD, by refining the lattice.

• Here we observe that in quantum gravity the two procedures may well be the same.
• We outline the combinatorial structure of spinfoam quantum gravity, define the continuum limit, and show that under general conditions refining foams is the same as summing over them.
• The conditions bear on the cylindrical consistency of the spinfoam amplitudes and on the presence of appropriate combinatorial factors, related to the implementation of diffeomorphisms invariance.