GROUP THEORY
PHYS 7143 -
summer 2021
This is an overview of the course; for daily details, go to the schedule.
class roster
May 18 - July 27
Speak up!
Feel free -at any time- to suggest topics that you would like to see covered in the course.
May 18-20
1. Linear algebra: vectors, matrices, eigenvalues
Lecture notes and problem set #1 (due Tuesday, May 25)
2. Projection operators
you got a new idea?
3. Don’t know group theory
Lecture notes and problem set #2 (due Tuesday, May 25)
May 25-27
4. Finite groups - definitions
5. Group representations
Lecture notes and problem set #3 (due Tuesday, June 1)
6. Schur's Lemma
Our competition: MIT 18.085 Computational Science and Engineering I
June 1-3
7. Wonderful Orthogonality Theorem
Lecture notes and problem set #4 (due Tuesday, June 8)
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 (due Tuesday, June 8)
June 8-10
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 (due Tuesday, June 15)
12. Fundamental domain
June 15-17
13. Lorenz to Van Gogh
Lecture notes and problem set #7 (due Tuesday, June 22)
14. Diffusion confusion
lecture on line
15. Space groups
Lecture notes and problem set #8 (due Tuesday, June 22)
June 22-24
16. Space groups
17. Continuous groups
Lecture notes and problem set #9 (due Tuesday, June 29)
18. Lie groups
June 29 - July 1
19. Lie groups, matrix representations
Lecture notes and problem set #10 (due Thursday, July 8)
20. Lie groups, algebras, SO(2) and O(2)
21. SU(2) and SO(3)
Lecture notes and problem set #11 (due Thursday, July 8)
July 5-6
Summer Break
July 8
22. SU(2) and SO(3)
July 13-15
23. SO(4) = SU(2) x SU(2), Lorentz group
Lecture notes and problem set #12 (due Tuesday, July 20)
24. SO(1,3) spinors
25. Representations of simple algebras
Lecture notes and problem set #13 (due Tuesday, July 20)
July 20-22
26. Cartan construction of SU(3) irreps
27. Flavor SU(3)
Lecture notes and problem set #14 (due Tuesday, July 27)
28. Gell-Mann--Okubo formula
July 27
29. Wigner 3- and 6-j coefficients
Lecture notes and problem set #16 (optional, not graded)
bonus (last lecture)
30. Many particle systems. Young tableaux
Lecture notes and problem set #15 (optional, not graded)
July 29
Reading period
fancy footwork
symmetries : what are they good for?
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Overview of the course
The full set of lecture notes for the course (as of July 29, 2021), including the week 17 overview of what might be included into the final.
August 5
final exam 11:20am ‐ 2:10pm
instructions
August 9
Grades due at noon