Group theory provides the natural language to formulate symmetry principles and to describe their consequences in Mathematics and Physics. For example, the "special functions" of mathematical physics originate from underlying symmetries of the problem although their traditional presentation may not stress this universal feature. Modern developments in all branches of physics ranging from condensed-matter to high-energy physics emphasize the role of symmetries, thus highlighting the central importance of group theory.
This class gives an introduction to group theory and its applications in physics. An important tool is representation theory that provides a description of physical systems that is adapted to its symmetries. A highlight will be the Wigner-Eckart theorem which exploits the symmetry of a problem to characterize matrix elements and selection rules. For concreteness, examples will often be stimulated by solid-state physics, though the concepts are equally useful in many other areas of physics.
The class will follow the classic textbook by McWeeny that provides a self-contained well-written introduction to the material. Interested students will benefit the most from this class if they are acquainted with quantum mechanics at the level of Phys 660.