Spinfoam theories are hoped to provide the dynamics of non-perturbative loop
quantum gravity. But a number of their features remain elusive. The best
studied one -the euclidean Barrett-Crane model- does not have the boundary
state space needed for this, and there are recent indications that,
consequently, it may fail to yield the correct low-energy $n$-point functions.
These difficulties can be traced to the SO(4) -> SU(2) gauge fixing and the way
certain second class constraints are imposed, arguably incorrectly, strongly.
We present an alternative model, that can be derived as a bona fide
quantization of a Regge discretization of euclidean general relativity, and
where the constraints are imposed weakly. Its state space is a natural subspace
of the SO(4) spin-network space and matches the SO(3) hamiltonian spin network
space. The model provides a long sought SO(4)-covariant vertex amplitude for
loop quantum gravity.
Description
[0705.2388] The loop-quantum-gravity vertex-amplitude
%0 Journal Article
%1 Engle2007
%A Engle, Jonathan
%A Pereira, Roberto
%A Rovelli, Carlo
%D 2007
%K LQG spinfoam
%T The loop-quantum-gravity vertex-amplitude
%U http://arxiv.org/abs/0705.2388
%X Spinfoam theories are hoped to provide the dynamics of non-perturbative loop
quantum gravity. But a number of their features remain elusive. The best
studied one -the euclidean Barrett-Crane model- does not have the boundary
state space needed for this, and there are recent indications that,
consequently, it may fail to yield the correct low-energy $n$-point functions.
These difficulties can be traced to the SO(4) -> SU(2) gauge fixing and the way
certain second class constraints are imposed, arguably incorrectly, strongly.
We present an alternative model, that can be derived as a bona fide
quantization of a Regge discretization of euclidean general relativity, and
where the constraints are imposed weakly. Its state space is a natural subspace
of the SO(4) spin-network space and matches the SO(3) hamiltonian spin network
space. The model provides a long sought SO(4)-covariant vertex amplitude for
loop quantum gravity.
@article{Engle2007,
abstract = { Spinfoam theories are hoped to provide the dynamics of non-perturbative loop
quantum gravity. But a number of their features remain elusive. The best
studied one -the euclidean Barrett-Crane model- does not have the boundary
state space needed for this, and there are recent indications that,
consequently, it may fail to yield the correct low-energy $n$-point functions.
These difficulties can be traced to the SO(4) -> SU(2) gauge fixing and the way
certain second class constraints are imposed, arguably incorrectly, strongly.
We present an alternative model, that can be derived as a bona fide
quantization of a Regge discretization of euclidean general relativity, and
where the constraints are imposed weakly. Its state space is a natural subspace
of the SO(4) spin-network space and matches the SO(3) hamiltonian spin network
space. The model provides a long sought SO(4)-covariant vertex amplitude for
loop quantum gravity.
},
added-at = {2010-02-14T22:30:34.000+0100},
author = {Engle, Jonathan and Pereira, Roberto and Rovelli, Carlo},
biburl = {https://www.bibsonomy.org/bibtex/29dca86a04648497d131bc0ef362e019c/random3f},
description = {[0705.2388] The loop-quantum-gravity vertex-amplitude},
interhash = {60ec7a15016ca9e8454326e767e2439d},
intrahash = {9dca86a04648497d131bc0ef362e019c},
keywords = {LQG spinfoam},
note = {cite arxiv:0705.2388
Comment: 6pages},
timestamp = {2010-02-14T22:30:35.000+0100},
title = {The loop-quantum-gravity vertex-amplitude},
url = {http://arxiv.org/abs/0705.2388},
year = 2007
}