Groups and Symmetries (PHY 810)

PROF. T. SCHAEFER

This is a course on Symmetries in Physics aimed at graduate and advanced undergraduate students. Familiarity with quantum mechanics and classical field theory is useful but not absolutely necessary. The aim of the class is to acquaint the student with the uses of symmetry in modern physics. We will focus on the ways in which symmetries manifest themselves in physics. This includes exact global symmetries (such as rotational symmetry or Lorentz invariance), weakly broken global symmetries (such as isospin and flavor in particle physics), spontaneously broken global symmetries and the dynamics of Goldstone modes, and finally spontaneously broken local symmetries and the Higgs mechanism.

Outline

**Discrete Groups**

**Symmetries in Quantum Mechanics**

**Lie Algebras: SU(2) and Isospin**

**More on Representations: Tensors, Roots and Weights**

**SU(3): Color and Flavor**

**Spontaneous Symmetry Breaking**

**Higgs Mechanism**

Course Information: [postscript]

- Homework assignment 1 [postscript,pdf]

Clebsch Gordon Coefficients [postscript,pdf] - Homework assignment 2 [postscript,pdf]

- Homework assignment 3 [postscript,pdf]

- Practice test [postscript,pdf]

Some interesting links:

- Finite groups at Mathworld
- From PDG: [Clebsch-Gordon Ceooeficients] [SU(n) Representations] [Quark Model]
- Lie Groups at Wikipedia
- A review for physicists: R. Slansky: Group Theory for Unified Model Building, [Appendices]
- A recent popular book on the history of group theory and Galois theory: Mario Livio: The equation that could not be solved

Questions? Send email to thomas_schaefer@ncsu_edu