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.

中文翻译：

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中超空间模型的量化。

我们对中超空间模型的量化进行了全面的回顾。尽管本文的主要焦点是量子方面，但我们还介绍了与这些模型的定义相关的几个经典观点。我们讨论了一些重要的问题，特别是使用对称临界性原理作为获得所需哈密顿公式的非常有用的工具。讨论了两种主要类型的缩减：涉及具有两个 Killing 矢量场的度量和球对称模型的缩减。我们还回顾了通过将物质场耦合到这些系统而获得的更通用的模型。在整篇论文中，我们分别讨论了使用几何动力学变量的标准量化和依赖环量子重力启发方法的标准量化。