Supervisor: Lars Bojer Madsen

Symmetries, also known as a physicist’s best friend, is a useful property in the description of many physical systems, classically as well a quantum mechanically. The mathematical language used to describe symmetries is group theory. Most physicists have probably at some point in their education encountered results of group theory maybe without knowing it.

In this colloquium, I will give a brief introduction of group theory and representation theory. I will then try to build the link between the abstract theory of groups and representations to the symmetries of a quantum mechanical system. 

The focus of this colloquium will not be the application of group and representation theory in a specific branch of physics. Rather, It will be an introduction of how groups and representations can quantify properties of a quantum mechanical system such as degeneracies and good quantum numbers. Hopefully this colloquium will give perspective on the usefulness of group theory in quantum mechanics.