Non-Abelian Discrete Symmetries in Particle Physics
Non-Abelian Discrete Symmetries in Particle Physics
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DOI：
10.1143/ptps.183.1
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发表时间：
2010-03
影响因子：
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通讯作者：
H. Ishimori;Tatsuo C. Kobayashi;H. Ohki;H. Okada;Yusuke Shimizu;M. Tanimoto
中科院分区：
文献类型：
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作者：
H. Ishimori;Tatsuo C. Kobayashi;H. Ohki;H. Okada;Yusuke Shimizu;M. Tanimoto
非阿贝尔离散群在粒子物理学中有着重要的作用，本文对它们的教学进行了综述。我们展示了许多具体群体的群论方面，如陈述，它们的张量积。我们解释如何获得，共轭类，字符，表示，和张量积为这些群体（有限数量）。对SN，AN，T ′，DN，QN，N（2 N2），N（3 N2），T7，N（3 N3）和N（6 N2）等粒子物理模型中的模型建立问题进行了讨论.我们还提出了典型的风味模型，通过使用A4，S4，和ESTA（54）组。离散群的破缺模式和多重态的分解对于非阿贝尔离散对称性的应用是非常重要的。我们讨论了非阿贝尔离散群的这些破缺模式，这是建模的有力工具。我们还简要地回顾了非阿贝尔离散对称的异常的路径积分方法。
We review pedagogically non-Abelian discrete groups, which play an important role in the particle physics. We show group-theoretical aspects for many concrete groups, such as representations, their tensor products. We explain how to derive, conjugacy classes, characters, representations, and tensor products for these groups (with a finite number). We discussed them explicitly for SN , AN , T ′, DN , QN , Σ(2N 2), ∆(3N2), T7, Σ(3N 3) and ∆(6N2), which have been applied for model building in the particle physics. We also present typical flavor models by using A4, S4, and ∆(54) groups. Breaking patterns of discrete groups and decompositions of multiplets are important for applications of the non-Abelian discrete symmetry. We discuss these breaking patterns of the non-Abelian discrete group, which are a powerful tool for model buildings. We also review briefly about anomalies of non-Abelian discrete symmetries by using the path integral approach.