Linking covariant and canonical loop quantum gravity: New solutions to the Euclidean scalar constraint

@article{Alesci2012LinkingCA,
  title={Linking covariant and canonical loop quantum gravity: New solutions to the Euclidean scalar constraint},
  author={Emanuele Alesci and Thomas Thiemann and Antonia Zipfel},
  journal={Physical Review D},
  year={2012},
  volume={86},
  pages={024017}
}
It is often emphasized that spin-foam models could realize a projection on the physical Hilbert space of canonical Loop Quantum Gravity (LQG). As a first test we analyze the one-vertex expansion of a simple Euclidean spin-foam. We find that for fixed Barbero-Immirzi parameter \gamma=1 the one vertex-amplitude in the KKL prescription annihilates the Euclidean Hamiltonian constraint of LQG. Since for \gamma=1 the Lorentzian part of the Hamiltonian constraint does not contribute this gives rise to… 

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