This graduate level course will focus on the physics of symmetry using the mathematics of group theory and representation theory. Symmetry is a fundamental concept throughout physics, be it particle physics and field theory, condensed matter physics, cosmology, quantum mechanics/quantum information or atomic and molecular physics.
The basic concepts of geometrical symmetry, finite groups and their representations will be covered. A physically oriented introduction will be given to Lie algebras and Lie groups and their representations. The emphasis throughout will be on the particular rather than the general. Familiar concepts from quantum mechanics will be used repeatedly - for example, the hydrogen atom spectrum and its symmetries will arise repeatedly during the study of Lie groups. Rather than develop the general theory of semi-simple compact Lie groups, the important concepts will be illustrated through particular examples. For example, the groups SO(2), SO(3), SU(2), SU(3) etc. as they arise in physics and their unique and distinctive features and representations.
Pre-requisites: Quantum Mechanics
References: Group theory in a nutshell for physicists, by A. Zee
Shattered Symmetry, by P. Thyssen and A. Ceulemans
Group Theory and Physics, by S. Sternberg