The diffeomorphism constraint operator in loop quantum gravity

Laddha, Alok; Varadarajan, Madhavan

Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/4362

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DC Field	Value	Language
dc.contributor.author	Laddha, Alok	-
dc.contributor.author	Varadarajan, Madhavan	-
dc.date.accessioned	2012-02-16T08:32:28Z	-
dc.date.available	2012-02-16T08:32:28Z	-
dc.date.issued	2011-10	-
dc.identifier.citation	Classical and Quantum Gravity, 2011, Vol.28, p195010	en
dc.identifier.issn	1361-6382 (Online)	-
dc.identifier.issn	0264-9381	-
dc.identifier.uri	http://hdl.handle.net/2289/4362	-
dc.description	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations) Also appairs in Journal of Physics : Conference Series, 2012, Vol.360, p012009	en
dc.description.abstract	We construct the smeared diffeomorphism constraint operator at finite triangulation from the basic holonomy- flux operators of Loop Quantum Gravity, evaluate its continuum limit on the Lewandowski- Marolf habitat and show that the action of the continuum operator provides an anomaly free representation of the Lie algebra of diffeomorphisms of the 3- manifold. Key features of our analysis include: (i) finite triangulation approximants to the curvature, $F_{ab}^i$ of the Ashtekar- Barbero connection which involve not only small loop holonomies but also small surface fluxes as well as an explicit dependence on the edge labels of the spin network being acted on (ii) the dependence of the small loop underlying the holonomy on both the direction and magnitude of the shift vector field (iii) continuum constraint operators which do {\em not} have finite action on the kinematic Hilbert space, thus implementing a key lesson from recent studies of parameterised field theory by the authors. Features (i) and (ii) provide the first hints in LQG of a conceptual similarity with the so called "mu- bar" scheme of Loop Quantum Cosmology. We expect our work to be of use in the construction of an anomaly free quantum dynamics for LQG.	en
dc.language.iso	en	en
dc.publisher	IOP Publishing Ltd.	en
dc.relation.uri	http://arxiv.org/abs/1105.0636	en
dc.relation.uri	http://dx.doi.org/10.1088/0264-9381/28/19/195010	en
dc.relation.uri	http://adsabs.harvard.edu/abs/2011CQGra..28s5010L	en
dc.rights	2011 IOP Publishing Ltd.	en
dc.title	The diffeomorphism constraint operator in loop quantum gravity	en
dc.type	Article	en
Appears in Collections:	Research Papers (TP)

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