PHY 406 Symmetries in Physics

Credit Hours: 4
Prerequisite: PHY 401, PHY 404, or equivalent

Finite groups. Compact and non-compact Lie groups and Lie algebras. Group representation theory.

syllabus

1. Symmetry in physics: examples and types of symmetry (invariance); continuous, discrete groups, tilings, invariant sets.
2. Examples of groups: Galileo group, permutations groups.
3. Formal definitions, axioms, basic theorems for finite groups. Abelian groups, simple, semisimple groups.
4. The semisimple finite groups of order 1 - 32.
5. The Cube group and its subgroups.
6. More formal group theory: subgroups, normal subgroups, factoring of groups.
7. Representation of Groups: trivial, faithful, irreducible representations. Group algebra. Unitary representations. How to find all irreducible representations of finite groups.
8. Continuous groups. Lie groups. Compactness. Lie algebras. Examples of SO(N), SU(N), U(N). Unitary and nonunitary representations.
9. Representation of Lie groups. SU(N) as example. Basic, adjoint representations.
10. Lagrangians and their invariance groups. Noether's theorem. The EM Lagrangian as example of gauge group. Nonabelian gauge groups.

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