# 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…

## 47 Citations

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