GROUP THEORY
PHYS 7143 -
spring 2019
Tu,Th 1:30 - 2:45 in Architecture (West) 260
birdtracks.eu/~predrag/courses/PHYS-7143-19
class roster
January 8 - April 24
Speak up!
Feel free -at any time- to suggest topics that you would like to see covered in the course.
January 8
1. Linear algebra: vectors, matrices, eigenvalues
Lecture notes and problem set #1 (due Tuesday, January 15)
January 10
2. Projection operators
you got a new idea?
January 15
3. Don’t know group theory
Lecture notes and problem set #2 (due Tuesday, January 22)
January 17
4. Finite groups - definitions
January 22
5. Group representations
Lecture notes and problem set #3 (due Tuesday, January 29)
January 24
6. Schur's Lemma
Our competition: MIT 18.085 Computational Science and Engineering I
January 29
7. Wonderful Orthogonality Theorem
Lecture notes and problem set #4 (due Tuesday, February 5)
January 31
8. Hard work builds character
Optional fun reading: Penrose and no need to learn all these "Greek" words
February 5
9. Irreps decomposition
Lecture notes and problem set #5 (due Tuesday, February 12)
February 7
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
February 12
11. Symmetries and dynamics
Lecture notes and problem set #6 (due Tuesday, February 19)
February 14
12. Fundamental domain
February 19
13. Lorenz to Van Gogh
Lecture notes and problem set #7 (due Tuesday, March 5)
February 21
14. Diffusion confusion
February 26, no class, lecture on line
15. Space groups
Lecture notes and problem set #8 (due Tuesday, March 5)
February 28, no class
16. Space groups
March 5
17. Continuous groups
Lecture notes and problem set #9 (due Tuesday, March 12)
March 7
18. Lie groups
March 12
19. Lie groups, matrix representations
Lecture notes and problem set #10 (due Tuesday, April 2)
March 14
20. Lie groups, algebras, SO(2) and O(2)
March 18-22
Spring Break
March 26
21. SU(2) and SO(3)
Lecture notes and problem set #11 (due Tuesday, April 2)
March 28
22. SU(2) and SO(3), lecturer: John Wood
Apri 2
23. SO(4) = SU(2) x SU(2), Lorentz group
Lecture notes and problem set #12 (due Tuesday, April 9)
April 4
24. SO(1,3) spinors
April 9
25. Representations of simple algebras
Lecture notes and problem set #13 (due Tuesday, April 16)
April 11
26. Cartan construction of SU(3) irreps
April 16
27. Flavor SU(3)
Lecture notes and problem set #14 (due Tuesday, April 23)
April 18
28. Gell-Mann--Okubo formula
April 23 (last lecture)
29. Wigner 3- and 6-j coefficients
Lecture notes and problem set #16 (optional, not graded)
bonus
xx. Many particle systems. Young tableaux
Lecture notes and problem set #15 (optional, not graded)
April 24
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 April 17, 2019), including the week 17 overview of what might be included into the final.
May 2
final exam 2:40pm ‐ 5:30pm
instructions
May 6
Grades due at noon