Quantum Field Theory

Prof. Mathias Scheurer

The lecture will start already in the first week of the semester, i.e., the first class will take place on Wednesday, April 9, 2025. The exercise classes will start in the second week (i.e., the first sheet will be due on Tuesday, April 15 2025 and discussed on Thursday/Friday April 17/18, 2025).

• Wednesday, 08:00 - 09:30, Lecture Hall 57.06, Pfaffenwaldring 57
• Friday, 09:45 - 11:15, Lecture Hall 57.06, Pfaffenwaldring 57

• The lecture and the tutorials will be given in English.
• The registration for the exercise groups will be open from Friday April 11, 2025, 13:30. To register, you need the Lecture Key given in the first lecture. Note that the registration is only possible from within the university network.
• If you assign a password at the registration, you can request your current scores here.

Recordings of the lectures can be accessed via ILIAS. The recordings should be seen as a service to those of you who cannot come on a specific date (e.g., due sickness etc.) or want to recap later. However, I highly recommend attending as many lectures as possible, to take advantage of the interactive nature of the classroom and learn with/from your peers. 

There will be an individual 30 mins oral exam at the end of the course. You can choose which chapter the first few questions will be about, but should expect that any topic covered in the lecture can be part of the exam.

To be able to take the oral exam, you have to pass the exercise class (see below). Students who have already obtained a suitable certificate from another lecturer must have it recognized by July 1, 2025 by sending it via E-Mail to Prof. Scheurer.

1. Altland & Simons, Condensed Matter Field Theory.
2. Piers Coleman, Introduction to Many-Body Physics.
3. Bruus & Flensberg, Many-Body Quantum Theory in Condensed Matter Physics.
4. Sachdev, Quantum Phase Transitions.
5. Abrikosov, Gorkov, & Dzylaoshinski, Methods of Quantum Field Theory in Statistical Physics.
6. Zinn-Justin, Quantum Field Theory and Critical Phenomena.
7. Wen, Quantum Field Theory of Many-Body Systems.
8. Peskin & Schroeder, An Introduction to Quantum Field Theory.
9. Ryder, Quantum Field Theory.

• The many-body path integral. The challenge of many-body quantum mechanics. Warm-up: the path integral of a single particle. Coherent states and Grassmann variables. Many-body field integrals. Matsubara sums. Free particles.

• Perturbation theory and diagrammatics. The idea of asymptotics. Interacting electrons. Random-phase approximation. Lindhard function. Screening. Self-energy.

• Hubbard-Stratonovich transformation. General idea. Different channels. Application: interacting electrons.

• Superconductivity. Phonon-induced electron-electron interaction. Field-theory of superconductivity. Higgs mechanism. Electromagnetism response of superconductors.

• Disordered electrons. Disorder ensembles. Replica theory. Finite lifetime of electrons.

• Quantum magnetism. Field theory for Ising model. Path integral for single spin and Wess-Zumino-Witten terms. Continuum field theory for Heisenberg ferromagnets and antiferromagnets. Spin liquids and emergent gauge fields.

• Particle physics. Review of relativistic quantum mechanics. Klein-Gordon and Dirac field theories. Standard model of particle physics.

The weekly exercises class will involve:
(1) Handing in solutions for those exercises labeled as "written"; these will be marked and discussed in the next tutorial. The deadline is Tuesday at 5:00 PM of the week where the problem set will be discussed. Please upload your solutions on ILIAS before the deadline.
(2) Virtual presentations: at the beginning of every tutorial, you can indicate on a list which parts of the exercises labeled as "oral" you have prepared and are willing to present. While everyone will get points for the parts signed up for, only one person will have to present it.

If any question on the exercise lists is not clear enough, please feel free to contact joao.sobral@itp3.uni-stuttgart.de for clarifications.

In order to pass the exercises, you need at least 50% of the points in (1) and 66% of the points in (2); furthermore, every student is required to present at least three times on the blackboard.

To visualize content of the lecture I will sometimes use Wolfram Mathematica. The files shown in the lecture will also be made available to you via ILIAS. While you are encouraged to play with them on your own computer, the ability to write code is not required for the assessment of the lecture. You can display the Mathematica files on your computer using the Wolfram Player for Notebooks.

Please let me know within the first three weeks of the semester (deadline April 25) if you want to participate in the "Vertiefung". The plan of the "Vertiefung" is to learn about the renormalization-group technique. To this end, we will have a "book club" during the semester (towards the end of the lecture period, to make sure you have the necessary basics – the precise week(s) will be announced).