Marcelo M. Amaral, Raymond Aschheim, Klee Irwin (2019)

We consider quantum transition amplitudes, partition functions and observables for 3D spin foam models within SU(2) quantum group deformation symmetry, where the deformation parameter is a complex fifth root of unity. By considering fermionic cycles through the foam we couple this SU(2) quantum group with the same deformation of SU(3), so that we have quantum numbers linked with spacetime symmetry and charge gauge symmetry in the computation of observables. The generalization to higher-dimensional Lie groups SU(N), G2 and E8 is suggested. On this basis we discuss a unifying framework for quantum gravity. Inside the transition amplitude or partition function for geometries, we have the quantum numbers of particles and fields interacting in the form of a spin foam network − in the framework of state sum models, we have a sum over quantum computations driven by the interplay between aperiodic order and topological order.