HX334400 Special Lectures in Physics(Mathematics for Physics E (Group Theory))

Hiroshima University Syllabus

Japanese

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
（Katakana）ブツリガクトクベツコウギ（ブツリスウガクイー（グンロン））

Subject Name in
English Special Lectures in Physics(Mathematics for Physics E (Group Theory))

Instructor MOROZUMI TAKUYA,TANAKA ARATA

Instructor
(Katakana) 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 E208

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
Program
(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
Evaluation
(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.

Text/Reference
Books,etc. 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
Class,etc. 　

(More Details)

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review 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

Message

Other

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.

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 （Katakana）	ブツリガクトクベツコウギ（ブツリスウガクイー（グンロン））
Subject Name in English	Special Lectures in Physics(Mathematics for Physics E (Group Theory))
Instructor	MOROZUMI TAKUYA,TANAKA ARATA
Instructor (Katakana)	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 E208
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 Program (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 Evaluation (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.
Text/Reference Books,etc.	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 Class,etc.
(More Details)
Learning techniques to be incorporated
Suggestions on Preparation and Review	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
Message
Other
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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