Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2024Year School of Science HX334400 Specialized Education 物理学特別講義（物理数学Ｅ（群論）） 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）） Special Lectures in Physics(Mathematics for Physics E (Group Theory)) MOROZUMI TAKUYA,TANAKA ARATA モロズミ　タクヤ,タナカ　アラタ 3rd-Year,  First Semester,  First Semester (1st) Tues3-4：SCI E211 Lecture Lectures with the black boardIn case of the online,  we use "Teams". 2.0 B : Japanese／English 3 : Undergraduate High-Intermediate 25 : Science and Technology 06 : Physics 3rd , 4th year undergraduate students 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). 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. 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. Lecture 1 (Tanaka)　Introduction: Group theory and PhysicsLecture 2（Tanaka）Basics of group theory I :  Elements, Subgroup, Conjugate elements and Class, Representations and their bases, Irreducible and reducible representationsLecture 3 (Tanaka) Basics of group theory II : Orthogonality relation, Character, Projection operatorLecture 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 GroupLecture 10(Morozumi）Generators and commutation relations, Lie AlgebraLecture 11(Morozumi）Fundamental representation, Adjoint represenation, Root, Weight DiagramLecture 12(Morozumi）SO(3),SU(2),Rotational Group, Pauli Matrix, Application: Spin angular momentum compositionLecture 13(Morozumi）SU(3)：Gell-Mann matrix, Lie algebra, Fundamental representation, Lecture 14(Morozumi) Application: Quark and Gluon : color degree of freedomLecture 15(Morozumi）Spontaneous broken symmetry and pions as Nambu Goldstone boson Lecture 16(Morozumi) Lorentz Group and spinorReport 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) 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. We recommend this class for the 3rd year students. However, for the deep understanding, it is also recommended for the 4th year students. 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%) 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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