Counting Rules of Nambu–Goldstone Modes

IF 14.3 1区 物理与天体物理 Q1 PHYSICS, CONDENSED MATTER Annual Review of Condensed Matter Physics Pub Date : 2019-04-01 DOI:10.1146/annurev-conmatphys-031119-050644
Haruki Watanabe
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引用次数: 49

Abstract

When global continuous symmetries are spontaneously broken, there appear gapless collective excitations called Nambu–Goldstone modes (NGMs) that govern the low-energy property of the system. The application of this famous theorem ranges from high-energy particle physics to condensed matter and atomic physics. When a symmetry breaking occurs in systems that lack the Lorentz invariance to start with, as is usually the case in condensed matter systems, the number of resulting NGMs can be lower than that of broken symmetry generators, and the dispersion of NGMs is not necessarily linear. In this article, we review recently established formulae for NGMs associated with broken internal symmetries that work equally for relativistic and nonrelativistic systems. We also discuss complexities of NGMs originating from space-time symmetry breaking. Along the way we cover many illuminating examples from various context. We also present a complementary point of view from the Lieb–Schultz–Mattis theorem.
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Nambu-Goldstone模式的计数规则
当全局连续对称性被自发打破时,就会出现被称为Nambu-Goldstone模式(NGMs)的无间隙集体激发,它控制着系统的低能量特性。这个著名定理的应用范围从高能粒子物理到凝聚态物质和原子物理。当对称性破缺发生在缺乏洛伦兹不变性的系统中时,就像在凝聚态系统中通常发生的那样,所产生的ngm的数量可能低于对称性破缺产生器的数量,并且ngm的色散不一定是线性的。在这篇文章中,我们回顾了最近建立的与破缺内部对称相关的ngm公式,这些公式同样适用于相对论和非相对论系统。我们还讨论了由时空对称性破缺引起的ngm的复杂性。在此过程中,我们涵盖了来自不同背景的许多有启发性的例子。我们还提出了利布-舒尔茨-马蒂斯定理的一个补充观点。
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来源期刊
Annual Review of Condensed Matter Physics
Annual Review of Condensed Matter Physics PHYSICS, CONDENSED MATTER-
CiteScore
47.40
自引率
0.90%
发文量
27
期刊介绍: Since its inception in 2010, the Annual Review of Condensed Matter Physics has been chronicling significant advancements in the field and its related subjects. By highlighting recent developments and offering critical evaluations, the journal actively contributes to the ongoing discourse in condensed matter physics. The latest volume of the journal has transitioned from gated access to open access, facilitated by Annual Reviews' Subscribe to Open initiative. Under this program, all articles are now published under a CC BY license, ensuring broader accessibility and dissemination of knowledge.
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