課程資訊
課程名稱
微分幾何及其在物理的應用
Introduction to differential geometry for physicists
開課學期
100-2
授課對象
理學院 物理學研究所
授課教師
蘇武沛
學分
2
全/半年
半年
必/選修
選修
上課時間
星期五 67
上課地點
新物 833
備註
「開放式課程」。總人數上限：20 人
課程大綱
課程概述
Introduction to tensor analysis in curvilinear coordinate systems, differential forms, differential
geometry, Berry's phase and other applications of geometrical ideas in physics
課程目標
To prepare the students for modern differential and integral calculus and their applications in modern
physics.
課程要求
修過應用數學一、應用數學二、應用數學三或高等微積分
elementary quantum mechanics
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參考書目
“Mathematical Methods for Physicists”, by Arfken and Weber, 6th Edition, Sections 2.10, 2.11, 4.8
“Differential Forms with Applications to the Physical Sciences”, by Harley Flanders,
“Mathematical Methods of Physics”, by Mathews and Walker, 2nd Edition, Chapter 15
“Modern Quantum Mechanics”, by J. J. Sakurai, Revised Edition, Supplement I: Adiabatic Change
and Geometric Phase
 “Solid State Physics”, by Grosso and Parracivini, Chapter VIII
 “A Mathematical Gift, I”, by K. Ueno, K. Shiga and S. Morita, Chapter 1: Invitation to Topology
 “Studies in Global Geometry and Analysis”, by S. S. Chern
 “Geometry, Topology and Physics”, by M Nakahara
 “Topology and Geometry for Physicists”, C. Nash and S. Sen
No.
項目
百分比
評量方式
1. Homework
50%
(僅供參考)
2. Presentation
20%
3. Exam
30%
說明
課程進度
週次
日期
單元主題
第1週
2/24
Organizational meeting, course overview
第2週
3/02
Euler characteristic, curvature of surface
第3週
3/09
Intuitive discussion of Gauss-Bonnet , Poincare-Hop theorems
第4週
3/16
Adiabatic principle and Berry phase
第5週
3/23
Berry’s curvature-analysis and topology
第6週
3/30
Classical tensor analysis, connection and curvature
第7週
4/06
Model of gauge interaction in electronic-nuclear systems
第8週
4/13
Differential forms
第9週
4/20
Homology and cohomology groups
第 10 週
4/27
Spin Hamiltonians and fiber bundles
第 11 週
5/04
Differential geometry of surface
第 12 週
5/11
Global geometry of surface
第 13 週
5/18
Geometry of fiber bundles
第 14 週
5/25
Characteristic classes
第 15 週
6/01
Harmonic forms
第 16 週
6/08
Index theorem-application to polyacetylene and graphene
第 17 週
6/15
Review