Linking covariant and canonical loop quantum gravity: New solutions to the Euclidean scalar constraint
Abstract
It is often emphasized that spinfoam models could realize a projection on the physical Hilbert space of canonical loop quantum gravity. As a first test, we analyze the onevertex expansion of a simple Euclidean spin foam. We find that for fixed BarberoImmirzi parameter γ=1, the onevertex amplitude in the Kaminski, Kisielowski, and Lewandowski prescription annihilates the Euclidean Hamiltonian constraint of loop quantum gravity [T. Thiemann, Classical Quantum Gravity 15, 839 (1998).]. Since, for γ=1, the Lorentzian part of the Hamiltonian constraint does not contribute, this gives rise to new solutions of the Euclidean theory. Furthermore, we find that the new states only depend on the diagonal matrix elements of the volume. This seems to be a generic property when applying the spinfoam projector.
 Publication:

Physical Review D
 Pub Date:
 July 2012
 DOI:
 10.1103/PhysRevD.86.024017
 arXiv:
 arXiv:1109.1290
 Bibcode:
 2012PhRvD..86b4017A
 Keywords:

 04.60.Ds;
 Canonical quantization;
 General Relativity and Quantum Cosmology
 EPrint:
 33 pages, several figures