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

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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: https://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.