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Symmetry Methods in Physics
·
Module 7
Advanced Lie Algebras: SU(3) and the Eightfold Way
1
Cartan Subalgebras, Roots, and Weights in su(2)
Define the Cartan subalgebra, roots, and weights for a semisimple Lie algebra, and construct the root and weight diagrams for su(2).
2
su(3) Root and Weight Diagrams
Construct the root and weight diagrams for the su(3) Lie algebra.
3
Highest Weight Theorem for SU(3)
State the theorem of the highest weight for classifying the irreducible representations of SU(3).
4
Weight Diagrams of SU(3) Representations
Construct and interpret the weight diagrams of the fundamental (3, 3-bar) and adjoint (8) representations of SU(3).
5
Dynkin Labels for SU(3) Irreducible Representations
Define Dynkin labels for SU(3) and use them to label low-dimensional irreducible representations.
6
Decomposing SU(3) Tensor Products with Young Tableaux
Use the Young tableaux method to decompose tensor products of SU(3) representations.
7
Casimir Operators of SU(3)
Identify the Casimir operators of SU(3) and determine their eigenvalues for a given representation.
8
Classifying Baryons and Mesons with SU(3) Flavor Symmetry
Apply SU(3) flavor symmetry to classify baryons and mesons via the Eightfold Way.
Previous module
Representations of SU(2) and Physical Applications
Next module
Symmetries in Crystalline Solids