Alesci E, Thiemann T, Zipfel A (2012)
Publication Status: Published
Publication Type: Journal article
Publication year: 2012
Publisher: AMER PHYSICAL SOC
Book Volume: 86
Journal Issue: 2
DOI: 10.1103/PhysRevD.86.024017
It is often emphasized that spin-foam models could realize a projection on the physical Hilbert space of canonical loop quantum gravity. 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 Kaminski, Kisielowski, and Lewandowski prescription annihilates the Euclidean Hamiltonian constraint of loop quantum gravity [T. Thiemann, Classical Quantum Gravity 15, 839 (1998).]. Since, for gamma = 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 spin-foam projector.
APA:
Alesci, E., Thiemann, T., & Zipfel, A. (2012). Linking covariant and canonical loop quantum gravity: New solutions to the Euclidean scalar constraint. Physical Review D - Particles, Fields, Gravitation and Cosmology, 86(2). https://dx.doi.org/10.1103/PhysRevD.86.024017
MLA:
Alesci, Emanuele, Thomas Thiemann, and Antonia Zipfel. "Linking covariant and canonical loop quantum gravity: New solutions to the Euclidean scalar constraint." Physical Review D - Particles, Fields, Gravitation and Cosmology 86.2 (2012).
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