Linking covariant and canonical LQG II: Spin foam projector

Understand

In a seminal paper, Kaminski, Kisielowski an Lewandowski for the first time extended the definition of spin foam models to arbitrary boundary graphs.

• This is a prerequisite in order to make contact to the canonical formulation of Loop Quantum Gravity (LQG) whose Hilbert space contains all these graphs.
• This makes it finally possible to investigate the question whether any of the presently considered spin foam models yields a rigging map for any of the presently defined Hamiltonian constraint operators.
• In the analysis of this would-be spin foam rigging map we are able to identify an elementary spin foam transfer matrix that allows to generate any finite foam as a finite power of the transfer matrix.