Quantum Field Theory

Dr. Nicolai Lang

Wednesday, 12. April 2023

• 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 (11:30-13:00). The lectures will be recorded as usual.

• 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:

The 5 additional lectures are part of the block course "Quantum Field Theory - Advanced Topics" (LV-Nr. 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.

There will be an oral examination at the end of the course. Details will be given in the lecture.

• 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.

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

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 self-study (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 four-vectors ...

Knowledge of relativistic quantum mechanics it not required; however, it is certainly helpful if you have seen the Klein-Gordon and Dirac equation before. I will briefly rederive the Dirac equation from a "field theory" point of view.

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 marked with * are part of the block course "Quantum Field Theory - Advanced Topics" (LV-Nr. 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.

Warning: We are well aware of the capabilities and limitations of state of the art transformer models. For example, here is how ChatGPT (GPT-4) 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.