By Hajime Ishimori,Tatsuo Kobayashi,Hiroshi Ohki,Hiroshi Okada,Yusuke Shimizu,Morimitsu Tanimoto
These lecture notes supply an academic overview of non-Abelian discrete teams and exhibit a few functions to concerns in physics the place discrete symmetries represent an immense precept for version construction in particle physics. While Abelian discrete symmetries are usually imposed so that it will keep watch over couplings for particle physics - particularly version development past the traditional version - non-Abelian discrete symmetries were utilized to appreciate the three-generation taste constitution specifically.
Indeed, non-Abelian discrete symmetries are thought of to be the main beautiful selection for the flavour region: version developers have attempted to derive experimental values of quark and lepton lots, and combining angles by means of assuming non-Abelian discrete taste symmetries of quarks and leptons, but, lepton blending has already been intensively mentioned during this context, besides. the potential origins of the non-Abelian discrete symmetry for flavors is one other subject of curiosity, as they could come up from an underlying conception - e.g. the string conception or compactification through orbifolding – thereby delivering a potential bridge among the underlying idea and the corresponding low-energy quarter of particle physics.
This textual content explicitly introduces and stories the group-theoretical features of many concrete teams and exhibits the best way to derive conjugacy periods, characters, representations, and tensor items for those teams (with a finite quantity) whilst algebraic family members are given, thereby permitting readers to use this to different teams of curiosity.
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Extra resources for An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists (Lecture Notes in Physics)
An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists (Lecture Notes in Physics) by Hajime Ishimori,Tatsuo Kobayashi,Hiroshi Ohki,Hiroshi Okada,Yusuke Shimizu,Morimitsu Tanimoto