A Lorentz-Covariant Connection for Canonical Gravity
We construct a Lorentz-covariant connection in the context of first order canonical gravity with non-vanishing Barbero-Immirzi parameter. To do so, we start with the phase space formulation derived from the canonical analysis of the Holst action in which the second class constraints have been solved...
Main Authors: | , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
National Academy of Science of Ukraine
2011-08-01
|
Series: | Symmetry, Integrability and Geometry: Methods and Applications |
Subjects: | |
Online Access: | http://dx.doi.org/10.3842/SIGMA.2011.083 |
id |
doaj-6285b7b3c2794a3aa776ce2478ed51ee |
---|---|
record_format |
Article |
spelling |
doaj-6285b7b3c2794a3aa776ce2478ed51ee2020-11-24T21:51:11ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592011-08-017083A Lorentz-Covariant Connection for Canonical GravityMarc GeillerMarc Lachièze-ReyKarim NouiFrancesco SardelliWe construct a Lorentz-covariant connection in the context of first order canonical gravity with non-vanishing Barbero-Immirzi parameter. To do so, we start with the phase space formulation derived from the canonical analysis of the Holst action in which the second class constraints have been solved explicitly. This allows us to avoid the use of Dirac brackets. In this context, we show that there is a ''unique'' Lorentz-covariant connection which is commutative in the sense of the Poisson bracket, and which furthermore agrees with the connection found by Alexandrov using the Dirac bracket. This result opens a new way toward the understanding of Lorentz-covariant loop quantum gravity.http://dx.doi.org/10.3842/SIGMA.2011.083canonical gravityfirst order gravityLorentz-invariancesecond class constraints |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Marc Geiller Marc Lachièze-Rey Karim Noui Francesco Sardelli |
spellingShingle |
Marc Geiller Marc Lachièze-Rey Karim Noui Francesco Sardelli A Lorentz-Covariant Connection for Canonical Gravity Symmetry, Integrability and Geometry: Methods and Applications canonical gravity first order gravity Lorentz-invariance second class constraints |
author_facet |
Marc Geiller Marc Lachièze-Rey Karim Noui Francesco Sardelli |
author_sort |
Marc Geiller |
title |
A Lorentz-Covariant Connection for Canonical Gravity |
title_short |
A Lorentz-Covariant Connection for Canonical Gravity |
title_full |
A Lorentz-Covariant Connection for Canonical Gravity |
title_fullStr |
A Lorentz-Covariant Connection for Canonical Gravity |
title_full_unstemmed |
A Lorentz-Covariant Connection for Canonical Gravity |
title_sort |
lorentz-covariant connection for canonical gravity |
publisher |
National Academy of Science of Ukraine |
series |
Symmetry, Integrability and Geometry: Methods and Applications |
issn |
1815-0659 |
publishDate |
2011-08-01 |
description |
We construct a Lorentz-covariant connection in the context of first order canonical gravity with non-vanishing Barbero-Immirzi parameter. To do so, we start with the phase space formulation derived from the canonical analysis of the Holst action in which the second class constraints have been solved explicitly. This allows us to avoid the use of Dirac brackets. In this context, we show that there is a ''unique'' Lorentz-covariant connection which is commutative in the sense of the Poisson bracket, and which furthermore agrees with the connection found by Alexandrov using the Dirac bracket. This result opens a new way toward the understanding of Lorentz-covariant loop quantum gravity. |
topic |
canonical gravity first order gravity Lorentz-invariance second class constraints |
url |
http://dx.doi.org/10.3842/SIGMA.2011.083 |
work_keys_str_mv |
AT marcgeiller alorentzcovariantconnectionforcanonicalgravity AT marclachiezerey alorentzcovariantconnectionforcanonicalgravity AT karimnoui alorentzcovariantconnectionforcanonicalgravity AT francescosardelli alorentzcovariantconnectionforcanonicalgravity AT marcgeiller lorentzcovariantconnectionforcanonicalgravity AT marclachiezerey lorentzcovariantconnectionforcanonicalgravity AT karimnoui lorentzcovariantconnectionforcanonicalgravity AT francescosardelli lorentzcovariantconnectionforcanonicalgravity |
_version_ |
1725880049920376832 |