Linking covariant and canonical loop quantum gravity: New solutions to the Euclidean scalar constraint (original) (raw)

ADS

;

• Thiemann, Thomas ;
• Zipfel, Antonia

Abstract

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 γ=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 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 spin-foam projector.

Publication:

Physical Review D

Pub Date:

July 2012

DOI:

10.1103/PhysRevD.86.024017

10.48550/arXiv.1109.1290

arXiv:

arXiv:1109.1290

Bibcode:

2012PhRvD..86b4017A

Keywords:

• 04.60.Ds;
• Canonical quantization;
• General Relativity and Quantum Cosmology

E-Print:

33 pages, several figures