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We review some approaches to the Hamiltonian dynamics of (loop) quantum gravity, the main issues being the regularization of the Hamiltonian and the continuum limit.
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Rovelli C., Speziale S., On the geometry of loop quantum gravity on a graph,
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2011
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Bonzom V., Freidel L., The Hamiltonian constraint in 3d Riemannian loop quantum gravity,
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Dittrich B., Ryan J.P., Phase space descriptions for simplicial 4D geometries,
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Laddha A., Varadarajan M., Hamiltonian constraint in polymer parametrized field theory,
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Laddha A., Varadarajan M., The diffeomorphism constraint operator in loop quantum gravity,
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Rovelli C., A new look at loop quantum gravity,
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Yu L., Semiclassical analysis of the Wigner
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Yu L., Littlejohn R.G., Semiclassical analysis of the Wigner
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