F8600 Lie Groups in Physics

Lectures: Mondays 15:00-17:00.

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

Course Plan, Spring 2025:

Monday 17.02.25
[L7] Chapter 2; [E7] 1+2.

Monday 24.02.25
[L7] Chapter 3 (p.14-18) + Appendix C; [E7] 3+4+5.

Monday 03.03.25
[L7] Chapter 3 (p.19-21); [E7] 6.

Monday 10.03.25
[L7] Chapter 4 (p.22).

Monday 17.03.25
[L7] Chapter 4 (p.23-25) + Schur Lemma; [E7] 8.

Monday 24.03.25
[L7] Chapter 5; [E7] 9+10.

Monday 31.03.25
[L7] Chapter 6 (p.31-33); [E7] 11.

Monday 07.04.25
[L7] Chapter 6 (p.34-38); [E7] 12+13+14.

Monday 14.04.25
20 minutes test/quiz; [L7] Chapter 7; [E7] 15+16+17.

Monday 21.04.25
Velikonoce.

Monday 28.04.25
[L7] Chapter 8 + Appendix D; [E7] 18.

Monday 05.05.25
[L7] Chapter 9; [E7] 19+20+21.

Monday 12.05.25
Last lecture. [L7] Chapter 10+11.

Monday 19.05.25
No lecture.

Monday 26.05.25
Last day of semester. Colloquiums/Student presentations.

Colloquium titles:
15:00 Alena: Killing vector fields of FLRW.
15:30 Beata: Goldstone theorem.
16:00 David: Lie bracket of vector fields.
16:30 Leontyna: SL(2,C)/Z_2 = SO^+(1,3,R)
17:00 Margareta: Conformal groups.

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.