MSc Physik / MSc Physics

Quantum Field Theory

SS 20

Important

Please sign up for this course on C@mpus (LV-Nr. 045550000).

Until further notice, this course is provided online via ILIAS.

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

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 non-abelian 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
  • Non-abelian 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. xx-yy).

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Lectures

No. Date Notes Topics
1 08.04.2020 PDF - Lagrangian and Hamiltonian formalism
- Symmetries
2 15.04.2020 PDF - Noether's theorem
- Energy-momentum tensor
3 17.04.2020 PDF - Quantization of the Klein-Gordon field
- The Klein-Gordon field in spacetime
4 22.04.2020 PDF - Causality of the Klein-Gordon field
- Feynman propagator of the Klein-Gordon field
5 24.04.2020 PDF - Notes on the Poincaré group
- The Dirac equation
- Free-particle solutions of the Dirac equation
6 29.04.2020 PDF - Dirac field bilinears
- Quantization of the Dirac field
7 06.05.2020 PDF - Spin and statistics
- The Dirac propagator
- Causality
- Discrete symmetries of the Dirac theory
8 08.05.2020 PDF - Interacting QFTs
- Perturbation expansion of correlation functions
- Wick's theorem
9 13.05.2020 PDF - Feynman diagrams
- Feynman rules
10 15.05.2020 PDF - Disconnected Feynman diagrams
- Vacuum energy
11 20.05.2020 PDF - Scattering cross sections
- S- and T-matrix
12 22.05.2020 PDF - S-matrix elements from Feynman diagrams
- Feynman rules for scattering amplitudes
13 27.05.2020 PDF - Wick's theorem for fermions
- The photon propagator
- Feynman rules for quantum electrodynamics
14 29.05.2020 PDF - Electron-electron scattering
- Electron-positron scattering
- The muon-antimuon production cross section
15 10.06.2020 PDF - Overview of radiative corrections
- Soft bremsstrahlung
- Formal structure of the electron vertex function
16 12.06.2020 PDF - The Landé g-factor
- Evaluation of the vertex integral
17 17.06.2020 PDF - Infrared divergences in first order
- Cancellation in arbitrary order
- The Sudakov form factor
18 19.06.2020 PDF - Källén–Lehmann spectral representation
- Field-strength renormalization
- Physical mass vs. bare mass
19 24.06.2020 PDF - Electric charge renormalization
- Dimensional regularization
- Vacuum polarization
20 26.06.2020 PDF - Systematics of UV-divergences
- Mass dimension and renormalizability
- Note on quantum gravity
21 01.07.2020 PDF - Bare perturbation theory
- Renormalized perturbation theory for Phi-4-theory and QED
22 03.07.2020 PDF - The path integral in quantum mechanics
- Derivation of the Schrödinger equation
- Correlation functions from path integrals for fields
23 08.07.2020 PDF - Faddeev-Popov gauge-fixing procedure
- Photon propagator
25 10.07.2020 PDF - Structure of the QED U(1) gauge symmetry
- Generalization to non-abelian gauge groups
- Yang-Mills Lagrangian
25 15.07.2020 PDF - Higgs mechanism for an abelian U(1) gauge theory
- Goldstone theorem
- Gauge-invariant formulation
26 17.07.2020 PDF - Glashow-Weinberg-Salam 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
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