Important
Lecturer
Begin of lecture
8. April 2020
Time and Date
 Wednesday, 08:00  09:30, Seminar Room 5.331, Pfaffenwaldring 57
 Friday, 14:00  15:30, 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
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
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 

1  08.04.2020   Lagrangian and Hamiltonian formalism  Symmetries 

2  15.04.2020   Noether's theorem  Energymomentum tensor 

3  17.04.2020   Quantization of the KleinGordon field  The KleinGordon field in spacetime 

4  22.04.2020   Causality of the KleinGordon field  Feynman propagator of the KleinGordon field 

5  24.04.2020   Notes on the Poincaré group  The Dirac equation  Freeparticle solutions of the Dirac equation 

6  29.04.2020   Dirac field bilinears  Quantization of the Dirac field 

7  06.05.2020   Spin and statistics  The Dirac propagator  Causality  Discrete symmetries of the Dirac theory 

8  08.05.2020   Interacting QFTs  Perturbation expansion of correlation functions  Wick's theorem 

9  13.05.2020   Feynman diagrams  Feynman rules 

10  15.05.2020   Disconnected Feynman diagrams  Vacuum energy 

11  20.05.2020   Scattering cross sections  S and Tmatrix 

12  22.05.2020   Smatrix elements from Feynman diagrams  Feynman rules for scattering amplitudes 

13  27.05.2020   Wick's theorem for fermions  The photon propagator  Feynman rules for quantum electrodynamics 

14  29.05.2020   Electronelectron scattering  Electronpositron scattering  The muonantimuon production cross section 

15  10.06.2020   Overview of radiative corrections  Soft bremsstrahlung  Formal structure of the electron vertex function 

16  12.06.2020   The Landé gfactor  Evaluation of the vertex integral 

17  17.06.2020   Infrared divergences in first order  Cancellation in arbitrary order  The Sudakov form factor 

18  19.06.2020   Källén–Lehmann spectral representation  Fieldstrength renormalization  Physical mass vs. bare mass 

19  24.06.2020   Electric charge renormalization  Dimensional regularization  Vacuum polarization 

20  26.06.2020   Systematics of UVdivergences  Mass dimension and renormalizability  Note on quantum gravity 

21  01.07.2020   Bare perturbation theory  Renormalized perturbation theory for Phi4theory and QED 

22  03.07.2020   The path integral in quantum mechanics  Derivation of the Schrödinger equation  Correlation functions from path integrals for fields 

23  08.07.2020   FaddeevPopov gaugefixing procedure  Photon propagator 

25  10.07.2020   Structure of the QED U(1) gauge symmetry  Generalization to nonabelian gauge groups  YangMills Lagrangian 

25  15.07.2020   Higgs mechanism for an abelian U(1) gauge theory  Goldstone theorem  Gaugeinvariant formulation 

26  17.07.2020   GlashowWeinbergSalam Theory  Higgs mechanism and mass generation  Quantum Chromodynamics 
Problem Sets
No.  Problem Set  Date  Comments 

1  Problem Set 01  08.04.2020  to be handed in via ILIAS until Friday, April 17 (recommended) or until the end of the lecture period (mandatory) 
2  Problem Set 02  17.04.2020  
3  Problem Set 03  24.04.2020  
4  Problem Set 04  01.05.2020  
5  Problem Set 05  08.05.2020  
6  Problem Set 06  15.05.2020  
7  Problem Set 07  22.05.2020  
8  Problem Set 08  29.05.2020  
9  Problem Set 09  12.06.2020  
10  Problem Set 10  19.06.2020  
11  Problem Set 11  26.06.2020  
12  Problem Set 12  03.07.2020  
13  Problem Set 13  10.07.2020 
Tutorials
Tutor  Room  Day  Time 

Jan Kumlin / Nastasia Makki  5.331  Friday  11:30  13:00 