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Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity

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Author(s): Valentin Bonzom | Alok Laddha

Journal: Symmetry, Integrability and Geometry : Methods and Applications
ISSN 1815-0659

Volume: 8;
Start page: 009;
Date: 2012;
Original page

Keywords: Hamiltonian constraint | loop quantum gravity | parametrized field theories | topological BF theory | discrete gravity

ABSTRACT
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. First, Thiemann's definition of the quantum Hamiltonian is presented, and then more recent approaches. They are based on toy models which provide new insights into the difficulties and ambiguities faced in Thiemann's construction. The models we use are parametrized field theories, the topological BF model of which a special case is three-dimensional gravity which describes quantum flat space, and Regge lattice gravity.
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