Quantum Field Theory

Dr. Nicolai Lang

Wednesday, 13. April 2022

• Wednesday, 08:00 - 09:30, Seminar Room 5.331, Pfaffenwaldring 57
• Friday, 09:45 - 11:15, Seminar Room 5.331, Pfaffenwaldring 57

• 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.

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).

Download PDF

You can also download a combined PDF including all blackboard notes of this course.