Aspects of Renormalization Group (PHY771, Spring 2020)


The class timings are

Lecture Notes


Jan 10, 2020

More details are given below. To summarize:

Please let me know if you have any other questions, topic suggestions or any other comments!

Course Description

The ideas of renormalization group (RG) are a fundamental aspect of our modern understanding of field theories. Besides providing a intuitive explanation for the otherwise mysterious tricks for removing infinities in quantum field theory (QFT), RG also provides a unifying framework for condensed matter physics and particle physics, and organizes several concepts in field theory.

In this course, we will go over the broad conceptual ideas and look at some concrete applications of RG to physical phenomenon, both in particle physics and condensed matter physics. We will introduce RG and use it to motivate (or “define”) field theory. On the condensed matter side, we will see how field theory arises from simple lattice models, explore how RG organizes ideas of critical phenomenon in CM, and helps us understand “universality.” On the particle physics side, it will clarify the meaning of renormalizabilty, tell us why the quark mass depends on the energy scale, etc. While we will also discuss some differences between the condensed matter and high energy point of view, most of our discussion will not depend on whether you live in real time (quantum field theory) or imaginary time (statistical field theory).


Quantum mechanics is necessary. QFT is not required, but will help. In fact, this might be a good place to learn QFT if you have never studied it, because RG can be used to define and motivate QFT. However, the course will be ideal if you have seen at least a semester of quantum field theory.


The topics to be covered are flexible and we can tailor it to the class interest. The sort of things I will cover might be:


I will prepare some (optional) problem sets. They will not be graded, but will supplement the material covered in lectures.


There will be no exams!


If you don’t wish to register, but are interested in just sitting in for the lectures, please send me an email and I can include you in the mailing list.