自旋泡沫：基础
Spinfoams: Foundations
AI总结：
本文综述了自旋泡沫的基础理论，重点介绍其在圈量子引力中实现四维微分同胚协变动力学的作用、与Regge微积分和拓扑量子场论的联系，并详细回顾了EPRL模型的推导、计算工具、扩展及领域内的成功与开放问题。
摘要：
自旋泡沫为圈量子引力的动力学提供了一个框架，该框架在广义相对论完整的四维微分同胚对称群下具有明显的协变性。通过这种方式，它们完善了三维微分同胚协变性的理想，这一理想在每一步都始终如一地推动着圈量子引力。具体而言，自旋泡沫模型旨在通过引力路径积分的离散化，提供一个投影算符，以及一个作用于圈量子引力所有约束的同时核上的物理内积。在小普朗克常数极限下，它们与Regge微积分的路径积分密切相关，同时保留了正则量子引力理论的所有工具。它们也可以被理解为拓扑量子场论中已被充分理解的状态和模型（state sum models）的推广。在本章中，我们回顾了自旋泡沫的所有这些方面，并详细回顾了目前最常用的自旋泡沫模型——EPRL模型的推导过程、其计算工具，以及文献中对其的各种扩展。此外，我们还总结了该领域的一些成功之处和未解决的问题。
英文摘要：
Spinfoams provide a framework for the dynamics of loop quantum gravity that is manifestly covariant under the full four-dimensional diffeomorphism symmetry group of general relativity. In this way they complete the ideal of three-dimensional diffeomorphism covariance that consistently motivates loop quantum gravity at every step. Specifically, spinfoam models aim to provide a projector onto, and a physical inner product on, the simultaneous kernel of all of the constraints of loop quantum gravity by means of a discretization of the gravitational path integral. In the limit of small Planck constant, they are closely related to the path integral for Regge calculus, while at the same time retaining all of the tools of a canonical quantum theory of gravity. They may also be understood as generalizations of well-understood state sum models for topological quantum field theories. In this chapter, we review all of these aspects of spinfoams, as well as review in detail the derivation of the currently most used spinfoam model, the EPRL model, calculational tools for it, and the various extensions of it in the literature. We additionally summarize some of the successes and open problems in the field.
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