F8600 Lie Groups in Physics

Lectures: Mondays 18:00-20:00.

Lectures take place in FLenc, room 03028, 3rd floor, building 6.

Course Plan, Spring 2023:

Monday 13.02.23
[L7] Chapter 2; [E7] 1+2.

Monday 20.02.23
[L7] Chapter 3 (p.14-18) + Appendix C; [E7] 3+4+5.

Monday 27.02.23 at 18:00
Cancelled.

Friday 03.03.23 at 8:00
[L7] Chapter 3 (p.19-21); [E7] 6.

Monday 06.03.23 at 18:00
[L7] Chapter 4 (p.22).

Monday 13.03.23
[L7] Chapter 4 (p.23-25); [E7] 8.

Monday 20.03.23
[L7] Chapter 5; [E7] 9+10.

Monday 27.03.23
[L7] Chapter 6 (p.31-33) + Schur Lemma + Casimirs; [E7] 11.

Monday 03.04.23 at 18:00
[L7] Chapter 6 (p.34-35).

Tuesday 11.04.23 at 8:00
[L7] Chapter 6 (p.36-38); [E7] 12+13+14.

Tuesday 18.04.23 at 8:00
Cancelled.

Wednesday 19.04.23 at 18:00
20 minutes test/quiz; [L7] Chapter 7; [E7] 15+16+17.

Tuesday 25.04.23 at 8:00
[L7] Chapter 8 + Appendix D; [E7] 18.

Tuesday 02.05.23 at 8:00
Cancelled.

Wednesday 03.05.23 at 18:00
[L7] Chapter 9; [E7] 19+20+21.

Tuesday 09.05.23 at 8:00
Last lecture. [L7] Chapter 10+11.

Tuesday 16.05.23
No lecture.

Tuesday 23.05.23
Colloquiums/Students presentations.

Colloquium titles:
8:30 Jan: Symplectic group.
9:00 Zdenek: SL(2,C)/Z_2 = SO^+(1,3,R).

Wednesday 31.05.23
Colloquiums/Students presentations.

Colloquium titles:
10:00 Amin: Quaternions and rotations.
Beata: ____________

Course Material:

[L7]: Gerard 't Hooft, "Lie Groups in Physics", lecture notes version 25.06.2007. Czech translation by Michal Lenc from 2004.
[E7]: Gerard 't Hooft, "Lie Groups Exercises", exercise notes version 18.06.2007. Czech translation by Michal Lenc from 24.06.2005.

NB: The Czech translations are not up to date and will not be used in the course. They are only included as a language help.

Supplementary References:

[RNC]: R.N. Cahn, "Semi-Simple Lie Algebras and Their Representations", 1984. PDF .
[PE]: Pavel Etingof, "Lie groups and Lie algebras", 2022. PDF .
[HO]: Hugh Osborn, "Group Theory Lecture Notes", 2008-2021. PDF .
[AE]: Alberto Elduque, "Lie Algebras Course Notes", 2005-2021. PDF .
[OS]: Orlin Stoytchev, "Topology of SO(3) For Kids", arXiv:2310.19665.