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FUF020 / FIM430 FUF020 / FIM430 Quantum field theory lp4 VT21 (7.5 hp)

Course is offered by the department of Physics

Contact details

Examiner and lecturer: Riccardo Catena.

Student representatives:

Course purpose

The purpose of this course is to provide the student with a self-contained introduction to Quantum Field Theory (QFT), with a focus on Quantum Electrodynamics (QED) - the relativistic quantum theory of the electromagnetic field. 

To achieve this goal, the student will learn methods the importance of which goes beyond the domain of QFT. These include the perturbative expansion of the S-matrix and the use of renormalisation (see learning objectives). 

As an application of QFT, we will calculate cross sections and decay rates for a number of important physics processes.

Schedule

TimeEdit

Note: due to the lack of availability of lecture rooms, two lectures now on TimeEdit will be rescheduled as indicated below:

1) 30/03 -> 20/05 

2) 13/04 -> 21/05 

Both rescheduled lectures will start at 13:15. 

Course literature

1) "An Introduction to Quantum Field Theory", Michael E. Peskin and Daniel V. Schroeder (Westview 1995); available at Cremona

2) "Quantum Field Theory", Franz Mandl and Graham Shaw (Wiley 2010)

3) "The Quantum Theory of Fields", Vol. 1, Steven Weinberg (Cambridge 1995)

While 1) is our main textbook, my lectures also rely on 2) and 3). I will use Weinberg's book only during the first lecture.

Course design

The course is organised in 20 lectures (of 1h and 45 min each). Each lecture will be held via Zoom, and taught live on the blackboard. In particular, there will be no pre-recorded video lectures or shared notes as an attempt to increase the interaction between student and lecturer. In order to attend these lectures, please use the Zoom link below:

https://chalmers.zoom.us/j/66476832234
Password: 540246

In preparation for the exam, students are encouraged to take notes and ask questions during the online lectures. 

As a part of the exam (see below), you will receive three problem sets through Canvas' assignments built-in function.

For each lecture, below I list the book sections I am referring too. Each lecture is also partly based on my own notes.

Lecture 1. From non-relativistic Quantum Mechanics to Quantum Field Theory

Weinberg book: Sec. 1.1

Lecture 2. From non-relativistic Quantum Mechanics to Quantum Field Theory

Weinberg book: Sec. 1.1

Peskin and Schroeder book: Sec. 2.1

Lecture 3. A first example: Non covariant quantisation of the electromagnetic field

Mandl and Shaw book: Secs. 1.2 and 1.4 

Lecture 4. Lagrangian Field Theory: canonical quantisation 

Mandl and Shaw book: Secs. 2.1 and 2.2

Peskin and Schroeder book: Sec. 2.2 

Lecture 5. Symmetries and conservation laws

Mandl and Shaw book: Secs. 2.3 and 2.4 

Peskin and Schroeder book: Secs. 2.2 and 3.1

Lecture 6. Symmetries and conservation laws

Mandl and Shaw book: Secs. 2.4 

Peskin and Schroeder book: 3.1 and 3.2

Lecture 7. The quantised real Klein-Gordon field

Mandl and Shaw book: Sec. 3.1 

Peskin and Schroeder book: Sec. 2.3

Lecture 8. The quantised real Klein-Gordon field

Mandl and Shaw book: Secs. 3.3 and 3.4

Peskin and Schroeder book: Secs. 2.3 and 2.4

Lecture 9. The quantised Dirac field

Peskin and Schroeder book: Secs. 3.2, 3.3 and 3.4

Mandl and Shaw book: Secs. 4.1 and 4.2

Lecture 10. The quantised Dirac field

Peskin and Schroeder book: Secs. 3.5 and 3.6

Mandl and Shaw book: Secs. 4.3 and 4.4

Lecture 11. Covariant quantisation of the electromagnetic field and the QED Lagrangian

Mandl and Shaw book: Secs. 5.1, 5.2, 5.3 and 4.5

Peskin and Schroeder book: Sec. 4.1

Lecture 12. Cross sections and the S-matrix 

Peskin and Schroeder book: Sec. 4.5

Lecture 13. LSZ reduction formula and correlation functions

Peskin and Schroeder book: Secs. 7.1 and 7.2

Lecture 14. Perturbative expansion of correlation functions

Peskin and Schroeder book: Secs. 4.2 and 4.3

Lecture 15. Diagrammatic representation of correlations functions

Peskin and Schroeder book: Sec. 4.4

Lecture 16. Perturbative expansion of the S-matrix 

Peskin and Schroeder book: Secs. 4.6 and 7.2

Mandl and Shaw book: Secs. 6.3, 7.1 and 7.2 

Lecture 17. Momentum space Feynman rules in QED and leading order applications

Mandl and Shaw book: Secs. 7.3, 7.4, 8.3, 8.4 and 8.6

Peskin and Schroeder book: Secs. 4.7, 5.1, 5.4 and 5.5

Lecture 18. Radiative corrections: Renormalisation

Mandl and Shaw book: Secs. 9.1, 9.2, 9.3 and 9.5

Peskin and Schroeder book: Secs. 7.1, 7.5 and 6.2

Lecture 19. Radiative corrections: Regularisation

Mandl and Shaw book: Secs. 10.1, 10.2, 10.3, 10.4 and 10.5

Peskin and Schroeder book: Secs. 6.2, 6.3, 7.1, and 7.5

Lecture 20. Infrared divergences, anomalous magnetic moments and unstable particles  

 

 

Changes made since the last occasion

New lecturer and examiner. 

Learning objectives and syllabus

By attending this course, the student is expected to acquire a solid knowledge of the following subjects in QFT:

- The transition from non-relativistic quantum mechanics to the relativistic theory of quantum fields

- Lagrangian field theory

- Free Klein-Gordon field

- Free Dirac field

- Free Maxwell field

- Interacting quantum fields

- Quantum Electrodynamics as a gauge theory

- Correlation functions

- Perturbative expansion of the S-matrix

- Feynman rules

- Cross sections and decay rates

- Lepton pair production in electron-positron collisions

- Moeller scattering, Bhabha scattering and Compton scattering

- Scattering by an external electromagnetic field

- Radiative corrections

- Renormalisation of Quantum Electrodynamics 

 

Examination form

The examination is divided into two mandatory parts (with grading weights given below):

1) Home problems organised in four sets with different deadline (weight: 40%). These will be uploaded on Canvas. Each set of problems assigns 40 points. 20 points in each set are required to be admitted to the oral exam.                                                      

2) Oral exam (weight: 60%). It consists in a 10 minute-long blackboard presentation on a topic chosen by the student among the ones addressed in the course followed by 40 minutes of questions on the concepts and equations discussed in the course. The student will be asked to re-derive some of these equations on the blackboard.        

Course summary:

Date Details Due