论文标题
$φ^4 $ - 理论的扭结简介
An introduction to kinks in $φ^4$-theory
论文作者
论文摘要
作为在所有物理学的不同领域中出现的一种低能量有效模型，无处不在的$φ^4 $ - 理论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，类似粒子的激发，这些激发在从宇宙学到粒子物理学和凝结物质理论的过程中起着核心作用。在这些讲义中，我们介绍了$φ^4 $ - 理论和控制其动态的各种物理过程的扭结描述。这些笔记针对高级本科生，重点是刺激对扭结动力学遇到的丰富现象学的定性见解。附录包含更详细的推导，并允许询问学生也可以获得定量的理解。涵盖的主题包括稳定解决方案的拓扑分类，扭结碰撞，bions的形成，扭结的共振散射以及扭结 - 脉冲相互作用。
As a low-energy effective model emerging in disparate fields throughout all of physics, the ubiquitous $φ^4$-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 $φ^4$-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.
