Lecturer
Begin of lecture
Wednesday, 13. April 2022
Time & Place
 Wednesday, 08:00  09:30, Seminar Room 5.331, Pfaffenwaldring 57
 Friday, 09:45  11:15, Seminar Room 5.331, Pfaffenwaldring 57
General Information
 The lecture and the tutorials will be given in English.
 There are two types of exercises: "Written" exercises are handed in in class and graded/corrected by the tutor. "Oral" exercises are discussed in the tutorials and presented by students on the blackboard.
 Admission to the final exam requires 80% of the written scores, 66% of the oral scores, and presenting a problem on the blackboard twice.
 Please register for the exercise groups online. To do so, you need the Lecture Key given in the first lecture.
 If you assign a password at the registration, you can request your current scores here.
Examination
There will be an oral examination at the end of the course. Details will be given in the lecture.
Literature
 Weinberg: The Quantum Theory of Fields (Volume 1)
Standard reference, very rigorous & mathematical, ratio #formulas/#text = high  Itzykson & Zuber: Quantum Field Theory
Standard reference, ratio #formulas/#text = high  Peskin & Schroeder: An Introduction to Quantum Field Theory
Standard reference for courses on QFT, ratio #formulas/#text = medium  Zee: Quantum Field Theory in a Nutshell
Compact and pedagogical introduction to the field, #formulas/#text = low
This course follows the exposition of Peskin & Schroeder.
Topics
The goal is to gain a thorough understanding of relativistic quantum field theory, the concepts of Feynman diagrams, renormalisation for quantum electrodynamics, and to extend this knowledge to nonabelian gauge theories. In particular:
 Relativistic quantum mechanics and Dirac equation
 Path integral formalism
 Quantisation  Free fields
 Interacting fields and Feynman diagrams
 Elementary processes and first corrections
 Renormalisation
 Nonabelian gauge fields
Requirements
The concept of second quantization is necessary to understand the quantization of fields. If you did not learn about second quantization in your advanced quantum mechanics course, I suggest that you catch up by selfstudy (any textbook on advanced quantum mechanics covers this topic). The same goes for the basic concepts of special relativity.
In particular, you should be familiar with the following concepts:
 Creation and annihilation operators
 Bosonic and fermionic (anti)commutation relations
 Constructing the bosonic/fermionic Fock space from the vacuum state (number states)
 Basics of special relativity: Lorentz group, Minkowski metric, Lorentz scalars and fourvectors ...
Knowledge of relativistic quantum mechanics it not required; however, it is certainly helpful if you have seen the KleinGordon and Dirac equation before. I will briefly rederive the Dirac equation from a "field theory" point of view.
Script
These notes follow mostly the exposition of Peskin & Schroeder. They are not an extension of the material covered in the lectures but the script that I use to prepare them. Please have a look at Peskin & Schroeder and the given references for more comprehensive coverage; the corresponding pages are noted in the headers (→ P&S • pp. xxyy).
Lectures
No.  Date  Notes  Topics (planned, may be subject to changes) 

1  13.04.22   Lagrangian and Hamiltonian formalism  Symmetries 

2  20.04.22   Noether's theorem  Energymomentum tensor 

3  22.04.22   Quantization of the KleinGordon field  The KleinGordon field in spacetime 

4  27.04.22   Causality of the KleinGordon field  Feynman propagator of the KleinGordon field 

5  29.04.22   The Dirac equation  Freeparticle solutions of the Dirac equation 

6  04.05.22   Dirac field bilinears  Quantization of the Dirac field 

7  06.05.22   Spin and statistics  The Dirac propagator  Causality  Discrete symmetries of the Dirac theory 

8  11.05.22   Interacting QFTs  Perturbation expansion of correlation functions  Wick's theorem 

9  13.05.22   Feynman diagrams  Feynman rules 

10  18.05.22   Disconnected Feynman diagrams  Vacuum energy  Scattering cross sections 

11  20.05.22   S and Tmatrix  
12  25.05.22   Smatrix elements from Feynman diagrams  Feynman rules for scattering amplitudes 

13  27.05.22   Wick's theorem for fermions  The photon propagator  Feynman rules for quantum electrodynamics 

14  01.06.22   Electronelectron scattering  Electronpositron scattering  The muonantimuon production cross section 

15  03.06.22   Overview of radiative corrections  Soft bremsstrahlung  Formal structure of the electron vertex function 

16  15.06.22   The Landé gfactor  Evaluation of the vertex integral 

17  17.06.22   Evaluation of the vertex integral (continued)  
18  22.06.22   Infrared divergence of the vertex function  Källén–Lehmann spectral representation 

19  24.06.22   Fieldstrength renormalization  Physical mass vs. bare mass 

20  29.06.22   Electric charge renormalization  Dimensional regularization 

21  01.07.22   Vacuum polarization  Lamb shift  Running of the finestructure constant  Landau pole and Dyson's argument 

22  06.07.22   Systematics of UVdivergences  Mass dimension and renormalizability  Note on quantum gravity 

23  08.07.22   Bare perturbation theory  Renormalized perturbation theory for Phi4theory 

24  13.07.22   The path integral in quantum mechanics  Derivation of the Schrödinger equation  The path integral for fields 

25  15.07.22   Correlation functions from path integrals  FaddeevPopov gaugefixing procedure  Photon propagator 

26  20.07.22   Structure of the QED U(1) gauge symmetry  Generalization to nonabelian gauge groups (1) 

27  22.07.22   Generalization to nonabelian gauge groups (2)  YangMills Lagrangian  Higgs mechanism for U(1) gauge theory (1)  Goldstone theorem 

28 (Bonus)  27.07.22   Higgs mechanism for U(1) gauge theory (2)  Structure of the Standard Model 

29 (Bonus)  29.07.22   GlashowWeinbergSalam Theory  Higgs mechanism in the Standard Model (1) 

30 (Bonus)  03.08.22   Higgs mechanism in the Standard Model (2)  Quantum Chromodynamics  Summary 
You can also download a combined PDF including all blackboard notes of this course.
Problem Sets
No.  Published  Due  Download  Comments 

1  13.04.22  22.04.22  
2  22.04.22  29.04.22  
3  29.04.22  06.05.22  
4  06.05.22  13.05.22  
5  13.05.22  20.05.22  
6  20.05.22  27.05.22  
7  27.05.22  03.06.22  
8  03.06.22  17.06.22  
9  17.06.22  24.06.22  
10  24.06.22  01.07.22  
11  01.07.22  08.07.22  
12  08.07.22  15.07.22  
13  15.07.22  22.07.22 
Tutorials
Tutor  Room  Day  Time 

Nastasia Makki  4.331  Friday  11:30  13:00 