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

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

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 mode...

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Bibliographic Details
Main Authors: Valentin Bonzom, Alok Laddha
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2012-03-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
Hamiltonian constraint
loop quantum gravity
parametrized field theories
topological BF theory
discrete gravity
Online Access:http://dx.doi.org/10.3842/SIGMA.2012.009
Description
Summary: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.
ISSN:1815-0659

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