Introduction to the operator product expansion

Course description

In this graduate course we will discuss the foundations of the operator product expansion and some interesting phenomenological results obtained from its application. The course consists of seven lectures, starting from February 23 until April 13 (note that April 6 is excluded because of the Easter break). Lectures will be held on Tuesdays, 2 pm to 4 pm, via Zoom. To sign up for the course, please write an email to and join the course on Ilias.

In this course the students will be introduced to the operator product expansion (OPE), with focus on its construction and applications. In the OPE a product of local operators is decomposed in an operator basis, and when used in a correlation function will produce a sum over long-distance matrix elements multiplied by short-distance Wilson coefficients. The students will learn the basics behind how this decomposition works and how to obtain perturbative Wilson coefficients as well as non-perturbative matrix elements. The students will see how the OPE is connected to sum rules via example calculations. Towards the end of the course, focus will be put on constructing an OPE in the presence of a background field to study magnetic moments.

Learning outcome:
The overall learning objective is thus to understand the main ideas behind the OPE and how to use it for phenomenological purposes.