Vol. 13 (2010) > lrr-2010-6

doi: 10.12942/lrr-2010-6
Living Rev. Relativity 13 (2010), 6

Quantization of Midisuperspace Models

1 Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid, Spain
2 Instituto Gregorio Millán, Grupo de Modelización y Simulación Numérica, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés, Spain

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Article Abstract

We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We cover some important issues, in particular, the use of the principle of symmetric criticality as a very useful tool to obtain the required Hamiltonian formulations. Two main types of reductions are discussed: those involving metrics with two Killing vector fields and spherically-symmetric models. We also review the more general models obtained by coupling matter fields to these systems. Throughout the paper we give separate discussions for standard quantizations using geometrodynamical variables and those relying on loop-quantum-gravity-inspired methods.

Keywords: Quantization, Loop quantum gravity, Midisuperspace, Quantum gravity

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Since a Living Reviews in Relativity article may evolve over time, please cite the access <date>, which uniquely identifies the version of the article you are referring to:

J. Fernando Barbero G. and Eduardo J. S. Villaseñor,
"Quantization of Midisuperspace Models",
Living Rev. Relativity 13,  (2010),  6. URL (cited on <date>):
http://www.livingreviews.org/lrr-2010-6

Article History

ORIGINAL http://www.livingreviews.org/lrr-2010-6
Title Quantization of Midisuperspace Models
Author J. Fernando Barbero G. / Eduardo J. S. Villaseñor
Date accepted 23 September 2010, published 14 October 2010
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