Theoretical Physics 3 (PHYC30022)

This subject will introduce topics in Theoretical Physics, including:

• Classical Field Theory: Action Principles and Noether’s Theorem. Electrodynamics and wave equations from action principle. Applications selected from: waves in media, dispersion relations, solitons, Kramers-Kronig relations, the Optical Theorem.
• Fluid Mechanics: Euler’s equation, the continuity equation and the Navier-Stokes equation. Rotational and irrotational flows. Turbulence and Reynolds’ numbers, and the onset of chaos. The Rayleigh-Taylor and other instabilities. Shock waves. The Kutta-Joukowski theorem and aerodynamics.
• Symmetry: Crystallography, point groups and space groups. Quasicrystals. Vibrational modes of molecules and molecular electronic structure. Crystal field theory. The uses of SU(2) in quantum mechanics. The SO(4) solution of the hydrogen atom. Relativistic invariance: the Lorentz and Poincare groups.