Title:	The diffeomorphism constraint operator in loop quantum gravity
Authors:	Varadarajan, Madhavan
Issue Date:	2012
Publisher:	IOP Science
Citation:	Journal of Physics Conference Series, 2012, Vol.360, p 012009
Abstract:	We construct the diffeomorphism constraint operator at finite triangulation from the basic holonomy- flux operators of Loop Quantum Gravity, and show that the action of its continuum limit 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 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.
Description:	Open Access.
URI:	http://hdl.handle.net/2289/5579
ISSN:	1742-6588 1742-6596(Online)
Alternative Location:	http://dx.doi.org/10.1088/1742-6596/360/1/012009
Copyright:	2012 IOP Science
Appears in Collections:	Research Papers (TP)

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