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An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists (Paperback, 2nd ed. 2022)
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An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists (Paperback, 2nd ed. 2022)
Series: Lecture Notes in Physics, 995
Expected to ship within 10 - 15 working days
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This lecture note provides a tutorial review of non-Abelian
discrete groups and presents applications to particle physics where
discrete symmetries constitute an important principle for model
building. While Abelian discrete symmetries are often imposed in
order to control couplings for particle physics-particularly model
building beyond the standard model-non-Abelian discrete symmetries
have been applied particularly to understand the three-generation
flavor structure. The non-Abelian discrete symmetries are indeed
considered to be the most attractive choice for a flavor sector:
Model builders have tried to derive experimental values of quark
and lepton masses, mixing angles and CP phases on the assumption of
non-Abelian discrete flavor symmetries of quarks and leptons, yet
lepton mixing has already been intensively discussed in this
context as well. Possible origins of the non-Abelian discrete
symmetry for flavors are another topic of interest, as they can
arise from an underlying theory, e.g., the string theory or
compactification via orbifolding as geometrical symmetries such as
modular symmetries, thereby providing a possible bridge between the
underlying theory and corresponding low-energy sector of particle
physics. The book offers explicit introduction to the group
theoretical aspects of many concrete groups, and readers learn how
to derive conjugacy classes, characters, representations, tensor
products, and automorphisms for these groups (with a finite number)
when algebraic relations are given, thereby enabling readers to
apply this to other groups of interest. Further, CP symmetry and
modular symmetry are also presented.
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