Group Theory
Vahid Karimipour
Sharif University of Technology
Description and Prerequisites
Group theory is the language by which we understand and analyze symmetry. Symmetry considerations lie at the foundation of many branches of physics. Therefore learning group theory is of utmost importance for any student of theoretical and experimental physics, no matter what is his field of study. Math I and II and Linear algebra are essential prerequisite for this course. Quantum mechanics I is also extermely useful.
Lecture Notes
These lecture notes are not complete and are being developed as I teach the course from time to time.
- Chapter 1: Basic concepts of group theory
- Chapter 2: Structures within a group, subgroups, cosets, and classes
- Chapter 3:Relations between different groups
- Chapter 4:Actions of a group on a set
- Chapter 5:Matrix groups
- Chapter 6:Continuous or topological groups
- Chapter 7:Lie groups and their Lie algebras
- Chapter 8:Representation theory of finite groups
- Chapter 9:Structure of Lie algebras
- Chapter 10:Cartan subalgebra, roots and Dynkin diagram, part I
- Chapter 11:Cartan subalgebra, roots and Dynkin diagram, part II
- Chapter 12:Classification of semi-simple Lie algebras
- Chapter 13:Representation theory of Lie algebras
