Hiroshima University Syllabus

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Academic Year 2024Year School/Graduate School School of Science
Lecture Code HX334400 Subject Classification Specialized Education
Subject Name 物理学特別講義(物理数学E(群論))
Subject Name
Subject Name in
Special Lectures in Physics(Mathematics for Physics E (Group Theory))
モロズミ タクヤ,タナカ アラタ
Campus   Semester/Term 3rd-Year,  First Semester,  First Semester
Days, Periods, and Classrooms (1st) Tues3-4:SCI E211
Lesson Style Lecture Lesson Style
(More Details)
Lectures with the black board
In case of the online,  we use "Teams".
Credits 2.0 Class Hours/Week   Language of Instruction B : Japanese/English
Course Level 3 : Undergraduate High-Intermediate
Course Area(Area) 25 : Science and Technology
Course Area(Discipline) 06 : Physics
Eligible Students 3rd , 4th year undergraduate students
Keywords Basics of group theory, Discrete Group(Symmetric Group, Alternating Group ,Point Group, Space Group), Continuous Group ((SO(3)),Lie Group, Angular momentum, operator ),  Molecular vibration and electron states, Crystal Field, Bloch’s theorem, Spin and SU(2), quark model and SU(3). 
Special Subject for Teacher Education   Special Subject  
Class Status
within Educational
(Applicable only to targeted subjects for undergraduate students)
In physics, the theory for the symmetries are important concept.  In this lecture, the basics and applications of the group theory for physics
Is presented. The contents of this lecture will be important for the other lectures such as Quantum mechanics III, elementary particle physics, Nuclear Physics, molecular physics, and condensed matter physics,  solid states structure and their properties,  solid state physics II, molecular physics,  continuum mechanics, Nuclear and particle physics, and relativistic quantum mechanics.
Criterion referenced
(Applicable only to targeted subjects for undergraduate students)
Class Objectives
/Class Outline
The purpose of this lecture is as follows.
Learn the basics of the group theory (the theory for the symmetries) which is relevant to physics. Learn and understand the methods of group theory which are applicable to the elementary particle physics, Nuclear Physics, molecular physics, and condensed matter physics.
Class Schedule Lecture 1 (Tanaka) 
Introduction: Group theory and Physics
Lecture 2(Tanaka)
Basics of group theory I :  Elements, Subgroup, Conjugate elements and Class, Representations and their bases, Irreducible and reducible representations
Lecture 3 (Tanaka)
Basics of group theory II : Orthogonality relation, Character, Projection operator
Lecture 4 (Tanaka)
Point groups (rotation, inversion, mirror, etc.), Space groups (symmetries in crystals)
Lecture 5 (Tanaka)
Crystal field (Electronic wave functions of atoms in crystal)
Lecture 6 (Tanaka)
Double groups (spin and double-valued irreducible representations, time reversal symmetry, Kramers' theorem)
Lecture 7 (Tanaka)
Electronic states for molecules (Molecular orbital method)
Lecture 8 (Tanaka)
Molecular vibrations (Symmetry for molecules and normal mode of vibration)
Lecture 9(Morozumi)
Introduction to continuous Group and Lie Group
Lecture 10(Morozumi)
Generators and commutation relations, Lie Algebra
Lecture 11(Morozumi)
Fundamental representation, Adjoint represenation, Root, Weight Diagram
Lecture 12(Morozumi)
SO(3),SU(2),Rotational Group, Pauli Matrix, Application: Spin
angular momentum composition

Lecture 13(Morozumi)
SU(3):Gell-Mann matrix, Lie algebra, Fundamental representation,
Lecture 14(Morozumi)
Application: Quark and Gluon : color degree of freedom
Lecture 15(Morozumi)
Spontaneous broken symmetry and pions as Nambu Goldstone boson
Lecture 16(Morozumi)
Lorentz Group and spinor

Report 100%.
In the lectures, we ask you to solve small questions. By submitting them as report, we will give the grade based on the reports. 
The followings are references. (not text). #=English book, the others are in Japanese.
*Gun to Hyogen (Kikkawa, Keiji, Iwanami)
*Bussei Butsuri Bussei Kagaku no tameno Gunron nyumon(Onodera Yoshitaka,Shokabo)
*Introduction to Lie Algebras   (Hajime Sato, Shokabo )
*#An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists (H. Ishimori, T. Kobayashi, H.Ohki, H. Okada, Y. Shimizu, M. Tanimoto, Springer )
*Kagaku ya Butsuri no tameno yasashii Gunron Nyumon(Fujinaga Shigeru, Narita Susumu, Iwanami)
*# Lie Algebra in Particle Physics(Howard Georgi)
*Gun to Butsuri  (Satou Hikaru, Maruzen)
*Renzoku Gunron Nyumon (Yamanouchi, Sugiura, Baifukan) 
PC or AV used in
(More Details)  
Learning techniques to be incorporated  
Suggestions on
Preparation and
We suggest you to review the contents of Quantum mechanics I and II, and the basic knowledge of matrix and vector in linear algebra I and II. 
Requirements We recommend this class for the 3rd year students. However, for the deep understanding, it is also recommended for the 4th year students.   
Grading Method In the lectures, we ask you to solve small questions. By submitting them as reports, we will give the grade based on the reports. Report(100%) 
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. 
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