We provide a pedagogical review article on fundamentals and applications of the quantum dynamics in strong electromagnetic fields in QED and QCD. The fundamentals include the basic picture of the Landau quantization and the resummation techniques applied to the class of higher-order diagrams that are enhanced by large magnitudes of the external fields. We then discuss observable effects of the vacuum fluctuations in the presence of the strong fields, which consist of the interdisciplinary research field of nonlinear QED. We also discuss extensions of the Heisenberg–Euler effective theory to finite temperature/density and to non-Abelian theories with some applications. Next, we proceed to the paradigm of the dimensional reduction emerging in the low-energy dynamics in the strong magnetic fields. The mechanisms of superconductivity, the magnetic catalysis of the chiral symmetry breaking, and the Kondo effect are addressed from a unified point of view in terms of the renormalization-group method. We provide an up-to-date summary of the lattice QCD simulations in magnetic fields for the chiral symmetry breaking and the related topics as of the end of 2022. Finally, we discuss novel transport phenomena induced by chiral anomaly and the axial-charge dynamics. Those discussions are supported by a number of appendices.

我们提供了一篇关于QED 和 QCD强电磁场中量子动力学的基础知识和应用的教学评论文章。基本原理包括朗道量化的基本图像和应用于高阶图类的恢复技术，这些高阶图通过大量的外部场得到增强。然后，我们讨论强场存在下真空涨落的可观测效应，其中包括非线性 QED 的跨学科研究领域。我们还讨论了海森堡-欧拉有效理论对有限温度/密度和非阿贝尔理论的扩展以及一些应用。接下来，我们继续讨论强磁场中低能动力学中出现的降维范式。超导机理、手性对称性破缺，和近藤效应通过重正化群方法从统一的角度得到解决。我们提供了截至 2022 年底手性对称性破缺的磁场中晶格 QCD 模拟以及相关主题的最新摘要。最后，我们讨论了由手性异常引起的新颖输运现象和轴向电荷动力学。这些讨论得到了许多附录的支持。