Wednesday, April 4, 2012

1204.0211 (Adam Henderson et al.)

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

Adam Henderson, Alok Laddha, Casey Tomlin
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.
View original: http://arxiv.org/abs/1204.0211

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