An introduction to non-Abelian discrete symmetries for particle physicists / Tatsuo Kobayashi [and four others].

Format:

Book

Author/Creator:

Kobayashi, Tatsuo (Physicist), author.

Series:

Lecture Notes in Physics

Lecture Notes in Physics ; v.995

Language:

English

Subjects (All):

Non-Abelian groups.

Mathematical physics.

Particles (Nuclear physics)--Multiplicity.

Particles (Nuclear physics).

Physical Description:

1 online resource (353 pages)

Edition:

Second edition.

Place of Publication:

Berlin, Germany ; New York, New York : Springer-Verlag, [2022]

Summary:

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.

Contents:

Intro

Preface to the Second Edition

Preface to the First Edition

Contents

1 Introduction

2 Basics of Finite Groups

3 SN

3.1 S3

3.2 S4

4 AN

4.1 A4

4.2 A5

5 T'

6 DN

6.1 DN with N= Even

6.2 DN with N= Odd

6.3 D4

6.4 D5

7 QN

7.1 QN with N=4n

7.2 QN with N=4n+2

7.3 Q4

7.4 Q6

8 QD2N

8.1 Generic Aspects

8.2 QD16

9 Σ(2N2)

9.1 Generic Aspects

9.2 Σ(18)

9.3 Σ(32)

9.4 Σ(50)

10 Δ(3N2)

10.1 Δ(3N2) with N/3 neq Integer

10.2 Δ(3N2) with N/3 = Integer

10.3 Δ(27)

10.4 Δ(48)

10.4.1 Conjugacy Classes and Tensor Products

10.4.2 The Different Bases of Δ(48)

11 TN

11.1 Generic Aspects

11.2 T7

11.3 T13 Group Theory

11.4 T19 Group Theory

12 Σ(3N3)

12.1 Generic Aspects

12.2 Σ(81)

13 Δ(6N2)

13.1 Δ(6N2) with N/3= Integer

13.2 Δ(6N2) with N/3= Integer

13.3 Δ(54)

13.4 Δ(96)

13.4.1 Conjugacy Classes

13.4.2 Characters and Representations

13.4.3 Tensor Products

14 Subgroups and Decompositions of Multiplets

14.1 S3

14.2 S4

14.3 A4

14.4 A5

14.5 T'

14.6 General DN

14.7 D4

14.8 General QN

14.9 Q4

14.10 QD2N

14.11 General Σ(2N2)

14.12 Σ(32)

14.13 General Δ(3N2)

14.14 Δ(27)

14.15 General TN

14.16 T7

14.17 General Σ(3N3)

14.18 Σ(81)

14.19 General Δ(6N2)

14.20 Δ(54)

15 Finite Subgroups of Continuous Groups

15.1 Finite Subgroups of SO(3)

15.1.1 SO(3)toDN

15.1.2 SO(3)toA4

15.1.3 SO(3)toS4

15.2 Finite Subgroups of SU(2)

15.2.1 SU(2)toQN

15.2.2 SU(2)toT'

15.3 Finite Subgroups of SU(3)

15.3.1 SU(3)toA4

15.3.2 SU(3)toA5

15.3.3 SU(3)toS4

15.3.4 SU(3)toDN

15.3.5 SU(3)toT'

15.3.6 SU(3)toΔ(3N2)

15.3.7 SU(3)toΔ(6N2)

16 Modular Symmetry

17 Automorphism

17.1 Z3

17.2 Z2timesZ'2

17.3 A4

17.4 Σ(18)

17.5 Δ(27).

18 Anomalies

18.1 Generic Aspects

18.2 Explicit Calculations

18.3 Comments on Anomalies

19 Non-Abelian Discrete Symmetry in Quark/Lepton Flavor Models

19.1 Neutrino Flavor Mixing and Neutrino Mass Matrix

19.2 A4 Flavor Symmetry

19.2.1 Realizing the Tri-Bimaximal Mixing of Flavors

19.2.2 Breaking Tri-Bimaximal Mixing

19.3 S4 Flavor Model

19.4 Alternative Flavor Mixing

19.5 Modular A4 Invariance and Neutrino Mixing

19.6 Comments on Other Applications

19.7 Comment on Origins of Flavor Symmetries

20 Generalized CP Symmetry

20.1 CP Transformation in Flavor Space

20.2 CP Violating Phase and Its Group Theoretical Origin

20.3 Modular Symmetry with Generalized CP Symmetry

20.3.1 CP Transformation of the Modulus τ

20.3.2 CP Transformation of Modular Multiplets

20.4 CP Violation by Modulus τ in A4 Model of Leptons

A Useful Theorems

B Representations of S4 in Several Bases

B.1 The Basis I

B.2 The Basis II

B.3 The Basis III

B.4 The Basis IV

C Representations of A4 in Different Basis

D Representations of A5 in Different Basis

D.1 The Basis I

D.2 The Basis II

E Representations of T' in Different Basis

E.1 The Basis I

E.2 The Basis II

F Representations of Δ(96) in Different Basis

G Other Smaller Groups

G.1 Z 4 Z4

G.2 Z 8 Z2

G.3 (Z2timesZ4)Z2 (I)

G.4 (Z2timesZ4)Z2 (II)

G.5 Z3 Z8

G.6 (Z6timesZ2) Z2

G.7 Z9 Z3

H Generators of the Modular Group

I Modular Forms.

Notes:

Description based on print version record.

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Kobayashi, Tatsuo An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists

ISBN:

3-662-64679-X

OCLC:

1302643596