Relating spin-foam to canonical loop quantum gravity by graphical calculus

The graphical calculus method is generalized to study the relation between covariant and canonical dynamics of loop quantum gravity. On one hand, a derivation partition function Euclidean Engle-Pereira-Rovelli-Livine (EPRL) spin-foam model presented. other action Hamiltonian constraint operator on certain spin network states calculated by method. It turns out that EPRL can provide rigging map such weakly satisfied physical for Immirzi parameter $\beta=1$. In this sense, formulations are consistent each other.