Department of Physics


Winter term 2017/2018:

Introduction to Renormalization with Applications in Condensed Matter

and High-Energy Physics

Time: Wednesdays 16:00 - 17:30 (Starting on October 11, 2017)

Place: 321 Seminarraum Theorie

Practice groups: Wednesdays 17:45 -


KLIPS2.0: Lecture - Details

Lecture notes:
Introduction to Renormalization with Applications in Condensed Matter and High-Energy Physics

Note: The lecture notes are still in a rather preliminary state and will be frequently updated. Please, let me know in case you find mistakes.

Problem sets:
- write me an email when you want to be informed about new problem sets or other things concerning the lecture!

Problem set 1
Problem set 2
Problem set 3

- Let me know in case you find mistakes.


In the lecture course I will give an introduction to the theory of the renormalization group. The renormalization group provides a connection between different physical theories on different scales and constitutes one of the basic concepts in theoretical physics. It is also a very powerful tool for the study of systems with many interacting degrees of freedom. The aim of the course is to introduce the main concepts and computational tools of the Renormalization Group. I will also cover some more formal aspects. Further, a range of applications of the renormalization group will be discussed touching many fields of physics such as solid state theory (high-temperature superconductors,...), condensed matter physics (cold atoms, Bose-Einstein condensation,...) and particle physics (QCD phase diagram, gravity,...).

  1. Introduction
    1. Phase transitions
    2. Critical phenomena
    3. Perturbative quantum field theory
    4. Renormalization-group based definition of QFTs
    5. QFTs in the high-energy limit
  2. Phase transitions and critical phenomena
    1. Ising model, XY model and Heisenberg model
    2. Universality and critical exponents
    3. Scaling hypothesis
    4. Correlations and hyperscaling
    5. Ginzburg-Landau-Wilson theory
    6. Perturbation theory and upper critical dimension
  3. Wilson's renormalization group
    1. Momentum-shell transformation
    2. epsilon expansion and the Wilson-Fisher fixed point
    3. Excursion: relations to QFTs in high-energy physics
    4. Landau-pole singularity and the triviality problem
    5. Fine-tuning and the hierarchy problem
  4. Functional integral approach to QFT
    1. Generating functional, effective action
    2. Perturbative renormalization
    3. Removal of divergencies
    4. Classification of perturbatively renormalizable theories
    5. Divergencies beyond one-loop level
    6. Callan-Symanzik equations and inductive proof of renormalizability
  5. Functional renormalization group
    1. Effective average action
    2. Wetterich equation
    3. Method of truncations
    4. Fixed points and stability matrix
    5. O(N) models and the functional RG (Mermin-Wagner theorem)
    6. Asymptotic safety scenario for non-perturbatively renormalizable QFTs (quantum gravity)
  6. Further applications of the functional renormalization group
    1. Topics depending on interest and time constraints


- I. Herbut, A Modern Approach to Critical Phenomena, Cambridge University Press.

- J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, Oxford University Press.

- P. Kopietz, L. Bartosch, F. Schütz, Introduction to the Functional Renormalization Group, Lecture Notes in Physics 798.

- J. Cardy, Scaling and Renormalization in Statistical Physics, Cambridge Lecture Notes in Physics.

Lecture notes

Introduction to Renormalization Group Theory (handwritten lecture notes, 2014)

Previous teaching activities

Winter term 2016/2017: Tutorial on Quantum Field Theory (Heidelberg University)

Winter term 2015/2016: Seminar on Quantum Mechanics (Heidelberg University)

Summer term 2015: Tutorial on Condensed Matter Theory (Heidelberg University)

Winter term 2014/2015: Lecture course on Renormalization Group Theory (Heidelberg University)

Summer term 2014: Seminar on Renormalization Group Theory (Heidelberg University)

February/March 2014: Lecture course on Quantum mechanics in a nutshell (AIMS South Africa)

Winter term 2013/2014: Lecture course on Renormalization Group Theory (Heidelberg University)