Speak up!
Feel free -at any time- to suggest topics that you would like to see covered in the course.
This is whiteboard strictly course, no projectors and slides. What follows are mostly clipps of lecture notes, many of which will be worked out in live time during the course. And no, revolution will not be televised, but when you see YouTube
icon, click on it to get a talking head
during the course, this homepage is updated hourly
Sources
- Group Theory : Birdtracks, Lie's, and Exceptional Groups Predrag Cvitanović
- The Special Unitary Group, Birdtracks, and Applications in QCD Judith M. Alcock-Zeilinger
- Birdtracks for SU(N) by Stefan Keppeler
Overview
17 June
Lecture 1-2 : try doing this without birdtracks!
- Sect 2.2 First example : SU(n), from birdtracks.eu
- Eigenvalues and eigenvectors
18 June
Lecture 3-4 : trace and multiplet bases
- Sect 2.2 First example : SU(n), finished
- SU(n), U(n) equivalence in adjoint rep (not done in the class)
- Trace bases, from Keppeler notes
- Sect 3 Permutations and the symmetric group, from Keppeler notes
- Groups, algebras; symmetric group
- Regular representation (not done in the class)
- Chap 6 (anti)-symmetrizers, from birdtracks.eu
- Sect 9.1 Two-index tensors, from birdtracks.eu
- Birdtracks, SO(3) example (from Keppeler notes, not done in the class)
19 June
Lecture 5-6 : multi-quark states
- Sect 9.2 Three-index tensors, from birdtracks.eu
- Young operators
- Trace of a birdtrack
- A non-hermitian example : Projection operators in 2D
- Hermitian conjugate of a birdtrack
- Representations of a group
- Regular representation
- Irreducible representations of the group algebra
- Irreducible representations of S_n
-
Definition : Identically and dimensionally zero operators :
- Tensor relations for small n
- Representations of SU(N) (from Alcock-Zeilinger course, not done in the class)
20 June
Lecture 7-8 : Lie groups and Lie algebras
- Invariants
-
Infinitesimal transformations, Lie algebras
- Lie groups for pedestrians
- Compact groups
- Matrix representations
- Group integrals
- Characters
- Hard work builds character
- Transformation of functions
22June
Lecture 9-10 : Wigner 3- and 6-j coefficients
you got a new idea?
22June
Bonus beach lecture : forget Feynman graphs
a "few" Saint-Jacut photos
beyond June
It takes class
- Discrete symmetries
- Definition : Matrix representation
- Subgroups, cosets, classes
- Table : group/class multiplication table D_3
- Class algebras
beyond June
Hard work builds character
- Schur's lemma
- Wonderful Orthogonality Theorem
- Example 2.5. Projection operators for cyclic group C_N
- It's all about class
- Invariant polynomials
beyond June
Adult birdtracks
- Negative dimensions
- Irreps of SO(n)
- Exer. 16.1. Gravity tensors
- Sect 2.3 Second xample : E_6 family, from birdtracks.eu
beyond June
Color space
Epilogue
Optional fun reading : Penrose and no need to learn all these "Greek" words
previous course reviews
