Quantization of Midisuperspace Models

J. Fernando Barbero G.  
Instituto de Estructura de la Materia, CSIC,
Serrano 123, 28006 Madrid, Spain

Eduardo J. S. Villaseñor  
Instituto Gregorio Millán,
Grupo de Modelización y Simulación Numérica,
Universidad Carlos III de Madrid,
Avda. de la Universidad 30, 28911 Leganés, Spain


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.

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