Quantization of Midisuperspace Models

TL;DR

This paper reviews the quantization of midisuperspace models, discussing classical foundations, reduction techniques, and various quantization methods including geometrodynamics and loop quantum gravity approaches.

Contribution

It provides a comprehensive overview of classical and quantum aspects of midisuperspace models, highlighting the use of symmetric criticality and different reduction techniques.

Findings

Comparison of geometrodynamical and loop quantum gravity quantizations.

Analysis of models with two Killing vectors and spherical symmetry.

Discussion of matter coupling in midisuperspace models.

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.