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Symmetry Methods in Physics
·
Module 6
Representations of SU(2) and Physical Applications
1
Irreducible Representations of su(2) via Highest Weight
Classify all irreducible representations of the su(2) algebra using the method of highest weight.
2
Irreducible Representation Matrix Elements for Spin j
Construct the (2j+1)-dimensional irreducible representation matrix elements for arbitrary spin j.
3
SU(2) Representations and Angular Momentum
Relate the irreducible representations of SU(2) to the quantum theory of angular momentum.
4
Clebsch-Gordan Series for SU(2) Tensor Products
Decompose tensor products of SU(2) representations using the Clebsch-Gordan series.
5
Clebsch-Gordan Coefficients: Simple Cases
Compute Clebsch-Gordan coefficients for the addition of angular momenta in simple cases.
6
Wigner-Eckart Theorem: Simplifying Matrix Elements
State and apply the Wigner-Eckart theorem to simplify the calculation of matrix elements of tensor operators.
7
Isospin Classification of Hadrons with SU(2) Symmetry
Apply SU(2) symmetry to describe the isospin classification of hadrons.
Previous module
Continuous Symmetries: Lie Groups and Lie Algebras
Next module
Advanced Lie Algebras: SU(3) and the Eightfold Way