Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 009, 50 pages      arXiv:1110.2157
Contribution to the Special Issue “Loop Quantum Gravity and Cosmology”

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

Valentin Bonzom a and Alok Laddha b
a) Perimeter Institute for Theoretical Physics, 31 Caroline St. N, ON N2L 2Y5, Waterloo, Canada
b) Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, PA 16802-6300, USA

Received October 11, 2011, in final form February 24, 2012; Published online March 07, 2012

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.

Key words: Hamiltonian constraint; loop quantum gravity; parametrized field theories; topological BF theory; discrete gravity.

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