论文标题
自旋和高性能计算
Spinfoams and high performance computing
论文作者
论文摘要
数值方法是在SpinFOAM理论中进行计算的强大工具。我们审查可用的主要框架，其定义和各种应用程序。我们从$ \ texttt {sl2cfoam-next} $开始，这是最先进的库，可有效计算基于增强剂分解的EPRL旋转泡沫振幅。我们还根据Spinfoam振幅的集成表示回顾了两种替代方法：首先，复杂临界点的数值计算发现了Spinfoam振幅中的弯曲几何形状，并提供了解决SpinFoam理论中平稳性问题的重要证据。最后，我们以EPRL Spinfoam繁殖器为例，基于Lefschetz Thimble和Markov-Chain Monte Carlo方法回顾了可观察到的期望值的数值估计。
Numerical methods are a powerful tool for doing calculations in spinfoam theory. We review the major frameworks available, their definition, and various applications. We start from $\texttt{sl2cfoam-next}$, the state-of-the-art library to efficiently compute EPRL spin foam amplitudes based on the booster decomposition. We also review two alternative approaches based on the integration representation of the spinfoam amplitude: Firstly, the numerical computations of the complex critical points discover the curved geometries from the spinfoam amplitude and provides important evidence of resolving the flatness problem in the spinfoam theory. Lastly, we review the numerical estimation of observable expectation values based on the Lefschetz thimble and Markov-Chain Monte Carlo method, with the EPRL spinfoam propagator as an example.
