关于自旋泡沫路径积分的莱斯胡什讲座
Les Houches lectures on Spinfoam Path Integrals
AI总结：
该文档是2025年莱斯胡什圈量子引力学校的讲义，对量子引力路径积分的自旋泡沫框架基础进行教学性回顾，从二维BF理论引入自旋泡沫路径积分，逐步构建到三维量子引力及四维广义相对论的量子化。
AI中文摘要：
在这些为2025年9月举行的莱斯胡什圈量子引力学校准备的讲义中，我们对量子引力路径积分的自旋泡沫框架基础进行了教学性回顾。在圈量子引力中，自旋网络态将三维空间的量子几何描述为纠缠体积量子的动态网络，而自旋泡沫利用广义相对论作为“几乎拓扑”场论的重新表述以及量子BF理论和拓扑态和的工具来定义这些自旋网络的跃迁振幅。讲座形式简短，共三次，每次一个半小时，仅涵盖了基础内容，并对更高级的研究方向做了简要介绍。我们从二维BF理论开始，为增加时空维度引入自旋泡沫路径积分，然后通过庞扎诺 - 雷格态和与图拉耶夫 - 维罗不变量构建三维量子引力，最后是四维广义相对论的量子化。
英文摘要：
In these lecture notes for the Les Houches School on Loop Quantum Gravity 2025, which took place in September 2025, we give a pedagogical review of the basics of the spinfoam framework for a quantum gravity path integral. While spin network states in loop quantum gravity describe the quantum geometry of the 3d space as dynamical networks of entangled quanta of volumes, spinfoams define transition amplitudes for those spin networks using the reformulation of general relativity as an "almost-topological" field theory and tools from quantum BF theory and topological state-sums. The lectures were a short format of three times one hour and a half, only allowing to cover the basics and offer a glimpse of more advanced lines of research. We introduce spin foam path integrals for increasing spacetime dimensions starting with 2d BF theory, then build up to 3d quantum gravity with the Ponzano-Regge state-sum and the Turaev-Viro invariant, and finally the quantization of general relativity in four dimensions.
