Non-Abelian Discrete Symmetries in Particle Physics
Hajime Ishimori,Tatsuo Kobayashi,Hiroshi Ohki,Yusuke Shimizu,Hiroshi Okada,Morimitsu Tanimoto +5 more
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TLDR
In this article, a review of pedagogically non-Abelian discrete groups, which play an important role in the particle physics, is presented, and the authors show group-theoretical aspects for many concrete groups, such as representations, characters, representations, and tensor products.Abstract:
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 $S_N$, $A_N$, $T'$, $D_N$, $Q_N$, $\Sigma(2N^2)$, $\Delta(3N^2)$, $T_7$, $\Sigma(3N^3)$ and $\Delta(6N^2)$, which have been applied for model building in the particle physics. We also present typical flavor models by using $A_4$, $S_4$, and $\Delta (54)$ 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.read more
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References
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Group Theory and its Applications to Physical Problems
Book
Lie algebras in particle physics
Howard Georgi,Richard Slansky +1 more
TL;DR: In this article, the classification theorem of SO(2n+1) and Spinors was applied to group theory, where SO(1+2n) and SO(3) were shown to be the classifiers of SU(1), SU(2) and SU(3).
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