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.

About Klee Irwin

Klee Irwin is an author, researcher and entrepreneur who now dedicates the majority of his time to Quantum Gravity Research (QGR), a non-profit research institute that he founded in 2009. The mission of the organization is to discover the geometric first-principles unification of space, time, matter, energy, information, and consciousness.


As the Director of QGR, Klee manages a dedicated team of mathematicians and physicists in developing emergence theory to replace the current disparate and conflicting physics theories. Since 2009, the team has published numerous papers and journal articles analyzing the fundamentals of physics.

Klee is also the founder and owner of Irwin Naturals, an award-winning global natural supplement company providing alternative health and healing products sold in thousands of retailers across the globe including Whole Foods, Vitamin Shoppe, Costco, RiteAid, WalMart, CVS, GNC and many others. Irwin Naturals is a long time supporter of Vitamin Angels, which aims to provide lifesaving vitamins to mothers and children at risk of malnutrition thereby reducing preventable illness, blindness, and death and creating healthier communities.

Outside of his work in physics, Klee is active in supporting students, scientists, educators, and founders in their aim toward discovering solutions to activate positive change in the world.  He has supported and invested in a wide range of people, causes and companies including Change.org, Upworthy, Donors Choose, Moon Express, Mayasil, the X PRIZE Foundation, and Singularity University where he is an Associate Founder.

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