### Fall 2014

# Introduction to Group Theory in Physics

### (Phys 790: Special Topics in Physics)

Roland Winkler

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.

### Textbook

*Symmetry: An Introduction to Group Theory and Its Applications*

by Roy McWeeny (Dover Books on Physics, 2002)
### Supplementary Course Material

All supplementary course materials and also homework
assignments will be posted on
blackboard.

Last modified: 2014-04-21 12:08:08
by Roland Winkler