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

EnglishSpecial 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 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

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 OutlineThe 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

ReviewWe 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.