Spin-Foams for All Loop Quantum Gravity

Understand

The simplicial framework of Engle-Pereira-Rovelli-Livine spin-foam models is generalized to match the diffeomorphism invariant framework of loop quantum gravity.

• The simplicial spin-foams are generalized to arbitrary linear 2-cell spin-foams.
• The resulting framework admits all the spin-network states of loop quantum gravity, not only those defined by triangulations (or cubulations).
• In particular the notion of embedded spin-foam we use allows to consider knotting or linking spin-foam histories.