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arXiv · 1204.0211

Constraint algebra in LQG reloaded : Toy model of a U(1)^{3} Gauge Theory I

Adam Henderson·Alok Laddha·Casey Tomlin
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Abstract

We analyze the issue of anomaly-free representations of the constraint algebra in Loop Quantum Gravity (LQG) in the context of a diffeomorphism-invariant gauge theory in three spacetime dimensions. We construct a Hamiltonian constraint operator whose commutator matches with a quantization of the classical Poisson bracket involving structure functions. Our quantization scheme is based on a geometric interpretation of the Hamiltonian constraint as a generator of phase space-dependent diffeomorphisms. The resulting Hamiltonian constraint at finite triangulation has a conceptual similarity with the "mu-bar"-scheme in loop quantum cosmology and highly intricate action on the spin-network states of the theory. We construct a subspace of non-normalizable states (distributions) on which the continuum Hamiltonian constraint is defined which leads to an anomaly-free representation of the Poisson bracket of two Hamiltonian constraints in loop quantized framework.

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Adam Henderson, Alok Laddha, Casey Tomlin. 2012-04-01. Constraint algebra in LQG reloaded : Toy model of a U(1)^{3} Gauge Theory I. https://doi.org/10.1103/physrevd.88.044028

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