Group theory I

  Teacher:  Professor You-Quan Li

2008-2009 semester ( >>Schedule )

     The main purpose of this course is to provide for graduated students whose major are "theoretical condensed matter physics" or "theoretical physics" the essential  knowledge of group theory and useful techniques applicable for solving physics problems. 

Tentative contents  (gray contents will be given in Group Theory II)

I. Basic Concepts

1. Introductory Concepts

II. Discrete Groups      

2. Finite Group Related to Symmetries in Physics

    [Crystallographic space group  (tables)  Point group symmetry  Crystal lattice structures]

3. Application Examples

4. Permutation Group, Braid Group and Knot theory

III. Continuous Groups

5. The Classical Group: Group of Transformation 

6. Lie Groups

7. Lie Groups and Lie Algebras

8. Topological Properties of Lie  Groups

9. Root Space and Dynkin Diagrams

10. Weight Space and Representations

IV* Advanced Topics

11. Affine Lie Algebras

12. Quantum Groups and Noncommutative Geometry

References

A.W. Joshi, Elements of Group Theory for Physicists, 2nd edition (John Wiley & Sons,) or 中译本《物理学中的群论基础》

J.P. Elliot & P.G. Dawber, Symmetry in Physics (the MacMillan Press)

R. Gilmore, Lie Group, Lie Algebra and Some of Their Applications, (Dover Publications)

S. Okubo, Introduction to Group Theory,

W. Ludwig and C. Falter, Symmetries in Physics, (Springer-Verlag, Berlin 1988)

J.F. Cornwell, Group Theory in Physics, (Academic Press, 2006)

马中骐，《物理学中的群论》；陶瑞宝，《物理学中的群论》

Wybourne，Classical Group and Its Applications， or 中译本《典型群及其应用》。

Download: Selected References for Graduate Course

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