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• W2149446905 abstract "In [1] we initiated an approach towards quantizing the Hamiltonian constraint in Loop Quantum Gravity (LQG) by requiring that it generates an anomaly-free representation of constraint algebra off-shell. We investigated this issue in the case of a toy model of a 2+1-dimensional $U(1)^{3}$ gauge theory, which can be thought of as a weak coupling limit of Euclidean three dimensional gravity. However in [1] we only focused on the most non-trivial part of the constraint algebra that involves commutator of two Hamiltonian constraints. In this paper we continue with our analysis and obtain a representation of full constraint algebra in loop quantized framework. We show that there is a representation of the Diffeomorphism group with respect to which the Hamiltonian constraint quantized in [1] is diffeomorphism covariant. Our work can be thought of as a potential first step towards resolving some long standing issues with the Hamiltonian constraint in canonical LQG." @default.
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• W2149446905 date "2013-08-20" @default.
• W2149446905 modified "2023-10-03" @default.
• W2149446905 title "Constraint algebra in loop quantum gravity reloaded. II. Toy model of an Abelian gauge theory: Spatial diffeomorphisms" @default.
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• W2149446905 doi "https://doi.org/10.1103/physrevd.88.044029" @default.
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