As a low-energy effective model emerging in disparate fields throughout all of physics, the ubiquitous $\varphi^4$-theory is one of the central models of modern theoretical physics. Its topological defects, or kinks, describe stable, particle-like excitations that play a central role in processes ranging from cosmology to particle physics and condensed matter theory. In these lecture notes, we introduce the description of kinks in $\varphi^4$-theory and the various physical processes that govern their dynamics. The notes are aimed at advanced undergraduate students, and emphasis is placed on stimulating qualitative insight into the rich phenomenology encountered in kink dynamics. The appendices contain more detailed derivations, and allow enquiring students to also obtain a quantitative understanding. Topics covered include the topological classification of stable solutions, kink collisions, the formation of bions, resonant scattering of kinks, and kink-impurity interactions.

中文翻译：

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$ \ varphi ^ 4 $-理论中的纽结介绍

作为遍及整个物理学的各个领域中出现的低能耗有效模型，无处不在的$ \ varphi ^ 4 $ -theory是现代理论物理学的中心模型之一。它的拓扑缺陷或扭结描述了稳定的类粒子激发，在从宇宙学到粒子物理学和凝聚态理论的过程中起着核心作用。在这些讲义中，我们介绍了$ \ varphi ^ 4 $-理论中的纽结描述以及控制其动力学的各种物理过程。这些注释针对的是高等本科生，重点是激发定性洞察力，以了解纽结动力学中遇到的丰富现象学。附录包含更详细的推导，并允许询问的学生也获得定量的理解。