Lecturer
Begin of course
Wednesday, 12. April 2023
Time & Place
 Wednesday, 08:00  09:30, Seminar Room 5.331, Pfaffenwaldring 57
 Friday, 09:45  11:15, Seminar Room 5.331, Pfaffenwaldring 57
The additional lectures on the Standard Model (mandatory for students who want to use QFT as "Schwerpunktmodul") take place in seminar room 5.331 (as the lecture) from Monday 24.07.23 till Friday 28.07.23 in the third block (11:3013:00). The lectures will be recorded as usual.
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.
Recordings of the lectures can be accessed via ILIAS.
This course can be used for the following modules:
Course  Module  Description  ECTS  Lectures 

MSc. Physik  107280  Schwerpunkt  12  131 (26+5 lectures) 
MSc. Physik  68030  Ergänzung  9  126 (26 lectures) 
MSc. Physics  68030  Semicompulsory  9  126 (26 lectures) 
The 5 additional lectures are part of the block course "Quantum Field Theory  Advanced Topics" (LVNr. 045575002) which takes place during the first week after the lecture period. These lectures are mandatory if you want to use the lecture as "Wahlpflichtmodul Schwerpunkt". In this case, the contents of these lectures will be part of the oral exam.
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  12.04.23   Lagrangian and Hamiltonian formalism  Transformations 

2  14.04.23   Symmetries  Noether's theorem  Energymomentum tensor 

3  19.04.23   Quantization of the KleinGordon field  The KleinGordon field in spacetime 

4  21.04.23   Causality of the KleinGordon field  Feynman propagator of the KleinGordon field 

5  26.04.23   The Dirac equation  
6  28.04.23   Freeparticle solutions of the Dirac equation  Dirac field bilinears  Quantization of the Dirac field 

7  03.05.23   Conserved charges  Spin and statistics  The Dirac propagator  Causality 

8  05.05.23   Discrete symmetries of the Dirac theory  Interacting QFTs 

9  10.05.23   Perturbation expansion of correlation functions  Wick's theorem 

10  12.05.23   Feynman diagrams  Feynman rules  Disconnected Feynman diagrams  Vacuum energy 

11  17.05.23   Scattering cross sections  S and Tmatrix 

12  19.05.23   Smatrix elements from Feynman diagrams  
13  24.05.23   Feynman rules for scattering amplitudes  Wick's theorem for fermions  The photon propagator  Feynman rules for quantum electrodynamics 

14  26.05.23   Electronelectron scattering  Electronpositron scattering  The muonantimuon production cross section 

15  07.06.23   The muonantimuon production cross section (continued)  Overview of radiative corrections  Soft bremsstrahlung 

16  09.06.23   Formal structure of the electron vertex function  The gfactor  Evaluation of the vertex integral 

17  14.06.23   Evaluation of the vertex integral (continued)  
18  16.06.23   Infrared divergence of the vertex function  Källén–Lehmann spectral representation 

19  21.06.23   Fieldstrength renormalization  Physical mass vs. bare mass 

20  23.06.23   Electric charge renormalization  Dimensional regularization 

21  28.06.23   Vacuum polarization  Lamb shift  Running of the finestructure constant  Landau pole and Dyson's argument 

22  30.06.23   Systematics of UVdivergences  Mass dimension and renormalizability  Note on quantum gravity 

23  05.07.23   Bare perturbation theory  Renormalized perturbation theory for Phi4theory 

24  07.07.23   Renormalized perturbation theory for QED  The path integral in quantum mechanics  Derivation of the Schrödinger equation 

25  12.07.23   The path integral for fields  Correlation functions from path integrals 

26  14.07.23   FaddeevPopov gaugefixing procedure  Photon propagator 

27  19.07.23   Structure of the QED U(1) gauge symmetry  Generalization to nonabelian gauge groups 

28  21.07.23   YangMills Lagrangian  Goldstone theorem 

29*  24.07.23   Higgs mechanism for U(1) gauge theory  Structure of the Standard Model 

30*  25.07.23   GlashowWeinbergSalam Theory (Part 1)  Weak isospin and hypercharge 

31*  26.07.23   GlashowWeinbergSalam Theory (Part 2)  Higgs mechanism in the Standard Model 

32*  27.07.23   Yukawa coupling  Quantum Chromodynamics  Summary 
Lectures marked with * are part of the block course "Quantum Field Theory  Advanced Topics" (LVNr. 045575002) which takes place during the first week after the lecture period. These lectures are mandatory if you want to use the lecture as "Wahlpflichtmodul Schwerpunkt". In this case, the contents of these lectures will be part of the oral exam.
Problem Sets
Warning: We are well aware of the capabilities and limitations of state of the art transformer models. For example, here is how ChatGPT (GPT4) solves Problem 1.2. It makes mistakes, but the results are undeniably impressive. In case you feel tempted: Contemplate why you decided to study physics in the first place, and why you signed up for this particular course. And, last but not least, remember the final exam.
No.  Published  Due  Download  Comments 

1  13.04.23  21.04.23  Problem Set 1  
2  20.04.23  28.04.23  Problem Set 2  
3  27.04.23  05.05.23  Problem Set 3  
4  04.05.23  12.05.23  Problem Set 4  
5  11.05.23  19.05.23  Problem Set 5  
6  18.05.23  26.05.23  Problem Set 6  
7  25.05.23  09.06.23  Problem Set 7  
8  08.06.23  16.06.23  Problem Set 8  
9  15.06.23  23.06.23  Problem Set 9  
10  22.06.23  30.06.23  Problem Set 10  
11  29.06.23  07.07.23  Problem Set 11  
12  06.07.23  14.07.23  Problem Set 12  
13  13.07.23    Problem Set 13 
Tutorials
Tutor  Room  Day  Time 

Johannes Mögerle  5.331  Friday  11:30  13:00 