Contact Information

address

Department of Physics Sharif University of Technology P. O. Box: 11155-9161 Tehran, Iran

e-mail:

vahid AT sharif.ir

Office Tel:

+98 21 66164524

Cell Phone:

+98 912 2972504

Group Theory (1394-1395)

  • Prerequisites:
  • Linear algebra is an essential prerequisite of this course. Quantum mechanics I is also extermely useful.

  • I follow my own lecture notes which you can download form this page. However as we go along, I may upgrade these lecture notes and post the revised note on this page. So you may want to wait until I possible revise each lecture note and then download the new ones. A list of other helpful references may be:
    • Group theory, by Joshi
    • Lie algebras in particle physics, Howard Georgi
    • Group theory for physicists, by Wybourne
  • Weekly schedule:
  • Saturday and Monday: 2:00 to 4:00 Pm

    Contents

    • Groups, matrix groups, permutation and braid groups, generators and relations.
    • structures within a group, subgroups, classes, cosets, factor groups, centers of a group, normalizers.
    • Homomorphism, Isomorphism, the fundamental theorem of Isomorphisms.
    • Action of a group on a manifold,
    • The general linear Matrix group and its subgroups.
    • Topological groups.
    • Manifolds and their tangent spaces, Lie groups and their Lie algebras, 
    • Representation theory of finite groups,
    • The structure of Lie Algebras, subalgebras, ideals, homomorphisms, solvable and nilpotent algebras, Killing form, simple and semi-simple algebras,
    • The structure of semi-simple Lie algebras, roots, simple roots, positive roots, Cartan basis, Dynkin diagrams,
    • Classification of simple Lie algebras and its proof.
    • Representation of Lie algebras.

     

     

Lecture Notes