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Journal Article

Constraint algebra in loop quantum gravity reloaded. II. Toy model of an Abelian gauge theory: Spatial diffeomorphisms

MPS-Authors

Tomlin,  Casey
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1210.3960
(Preprint), 357KB

PRD88_044029.pdf
(Any fulltext), 313KB

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Citation

Henderson, A., Laddha, A., & Tomlin, C. (2013). Constraint algebra in loop quantum gravity reloaded. II. Toy model of an Abelian gauge theory: Spatial diffeomorphisms. Physical Review D, 88(4): 044029. doi:10.1103/PhysRevD.88.044029.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000E-EE90-7
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.