2023-2024 / SPAT0162-1

Quantum field theory


20h Th, 10h Pr

Number of credits

 Master in space sciences (120 ECTS)4 crédits 


Jean-René Cudell

Language(s) of instruction

English language

Organisation and examination

Teaching in the first semester, review in January


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

Field theory course with an emphasis on quantum electrodynamics.


1. Maxwell's equations in relativistic form
2. The lagrangian of Electrodynamics and Noether's theorem
3. Symmetries, Noether theorem, Hamiltonian
4. Problems 1

5&6. Spin and the Lorentz group 
7. Poisson Brackets and canonical quantization
8. Problems 2

9. Second quantization, microcausality
10. Propagators, quantization of the Dirac field, quantization of the Maxwell field
11. Problems 3

12. Fermion and photon propagators. Interaction lagrangians and renormalisability. The concept of the S Matrix. Link with cross sections.
13. Evaluation of the matrix elements of T. Wick's theorem and Feynman rules.
14. Problems 4

15. Explicit example
16. QED Feynman rules, and the Rutherford cross section 
17. Crossing, Bhabba scattering, Møller scattering
18. Problems 5

19. The Compton cross section and related processes
20. Problems 6

Learning outcomes of the learning unit

The course has a double purpose: on the one hand, to give a practical knowledge of field theory, so that students can calculate the amplitudes for simple processes; on the other hand, to link field theory with particle and astroparticle physics.
At the end of the course, students will be able:
1) to understand the principles on which QED is built (Lorentz group, gauge invariance);
2) to derive Feynman rules from any interaction lagrangian;
3) to calculate elementary processes in QED and in scalar theories, for any energy;
4) to understand the concept of antiparticle.

Prerequisite knowledge and skills

Quantum mechanics, relativistic quantum mechanics.

Planned learning activities and teaching methods

This course is based on lectures,  and to discussion sessions where problems (see the course webpages for the list) are discussed, as shown in the table of contents. The problems will be solved by the students, under the guidance of the instructor. Preparing them is strongly advised.  

Mode of delivery (face to face, distance learning, hybrid learning)

The references for each lecture, notes and the list of problems are available on the course web pages.  

Recommended or required readings

Textbook : M.E. Peskin et D.V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley : 1995). Copies are available and will be distributed at the start of the course.

Exam(s) in session

Any session

- In-person

written exam ( open-ended questions ) AND oral exam

Additional information:

Written exam, followed by a discussion. The first question is on the theory, and the list of possible questions is available on the course web pages (it is subject to change during the year). The second question (given after the theory question is returned) is an open-book exercise. The written part lasts 4 hours.

Work placement(s)

Organisational remarks and main changes to the course

The course will be organised in 20 one-and-a-half-hour lectures/discussion sessions (see contents).


Jean-René Cudell
Institute of physics 19A Allée du 6 août Bldg B5a (4th floor, room 4/44) University of Liège Tel.: 04/3663654
E-mail: jr.cudell@ulg.ac.be
Web pages: http://www.theo.phys.ulg.ac.be

Association of one or more MOOCs