Group Theory
birdtracks.eu/course3
This is an overview of the course; for daily details, go to the schedule.
1. Linear algebra: vectors, matrices, eigenvalues
Lecture notes and problem set #1
2. Projection operators
you got a new idea?
3. Don’t know group theory
Lecture notes and problem set #2
4. Finite groups - definitions
5. Group representations
Lecture notes and problem set #3
6. Schur's Lemma
Our competition: MIT 18.085 Computational Science and Engineering I
7. Wonderful Orthogonality Theorem
Lecture notes and problem set #4
8. Hard work builds character
Optional fun reading: Penrose and no need to learn all these "Greek" words
9. Irreps decomposition
Lecture notes and problem set #5
10. It takes class
A fun read on group theory
we definitely will not cover: Marcus du Sautoy Finding Moonshine: A Mathematician's Journey Through Symmetry
11. Symmetries and dynamics
Lecture notes and problem set #6
12. Fundamental domain
13. Lorenz to Van Gogh
Lecture notes and problem set #7
14. Diffusion confusion
lecture on line
15. Space groups
Lecture notes and problem set #8
16. Space groups
17. Continuous groups
Lecture notes and problem set #9
18. Lie groups
19. Lie groups, matrix representations
Lecture notes and problem set #10
20. Lie groups, algebras, SO(2) and O(2)
21. SU(2) and SO(3)
Lecture notes and problem set #11
22. SU(2) and SO(3)
23. SO(4) = SU(2) x SU(2), Lorentz group
Lecture notes and problem set #12
24. SO(1,3) spinors
25. Representations of simple algebras
Lecture notes and problem set #13
26. Cartan construction of SU(3) irreps
27. Flavor SU(3)
Lecture notes and problem set #14
28. Gell-Mann--Okubo formula
29. Wigner 3- and 6-j coefficients
Lecture notes and problem set #16
30. Many particle systems. Young tableaux
Lecture notes and problem set #15
Reading period
fancy footwork
symmetries : what are they good for?
previous evaluations
Overview of the course
The full set of lecture notes for the course (as of July 29, 2021).