SU(N), Birdtracks and Applications in QCD

What is this course about?

This course aims at creating familiarity with the birdtrack formalism, which is a graphical method designed to dealing with representations of certain groups on (large) tensor product spaces. Our particular focus will be the representation theory of the group SU(N), which plays an important role in Quantum chromodynamics (QCD). At the end of the course, we will discuss some of these applications.

In this course, I hope to convey the importance of learning different formalisms, methods or "languages" to express already familiar topics, as a new viewpoint often furnishes the solutions to problems that seemed impossible in the familiar framework.

What are the prerequisites for this course?

You will need to be familiar with linear algebra, basic group theory (definition of a group, basic properties, definition of SU(N)) and basic definitions in algebra (definition of a module, definition of an algebra, etc., but I will briefly go over those in the course again as a reminder). You do not need to be familiar with representation theory, I will review the definitions and results needed for this course, but it will certainly be helpful if you have seen representation theory before. As to the applications in QCD, you do not need to have any prior knowledge as I will keep the discussions on applications fairly light, but if you happen to know some QCD it will be advandageous to you.

As already mentioned the main focus of this course is to learn the birdtrack formalism and how it can be used in practice when working with the group SU(N). Therefore, you do not need to know anything about the birdtrack formalism as this will be discussed in a lot of detail.

Will there be exercises?

Yes, from 2pm to 4pm on Fridays.