Course syllabus

Course-PM

FUF020 / FIM430 FUF020 / FIM430 Quantum field theory lp4 VT22 (7.5 hp)

Course is offered by the department of Physics

 

Contact details

Examiner: Riccardo Catena. e-mail: catena@chalmers.se;

Student representatives:

Måns Anduri, anduri@student.chalmers.se      
Johanna Brinkmalm, johbrink@student.chalmers.se    
Alva Kinman, alva.kinman@gmail.com   
Hanna Olvhammar, hanolv@student.chalmers.se      
Ludwig Scherqvist Halldner, halldner@student.chalmers.se    

 

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 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

 

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).

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

Peskin and Schroeder book: Sec. 2.1

Notes: Lecture_1.pdf

 

Lecture 2. A first example: Non covariant quantisation of the electromagnetic field

Mandl and Shaw book: Secs. 1.2 and 1.4 

Notes: Lecture_2.pdf

 

Lecture 3. Lagrangian Field Theory: canonical quantisation 

Mandl and Shaw book: Secs. 2.1, 2.2 and 2.3 

Peskin and Schroeder book: Sec. 2.2 

Notes: Lecture_3.pdf

 

Lecture 4. Symmetries and conservation laws

Mandl and Shaw book: Sec. 2.4 

Peskin and Schroeder book: Secs. 2.2, 3.1 and 3.2

Notes: Lecture_4.pdf

 

Lecture 5. The quantised real Klein-Gordon field

Mandl and Shaw book: Sec. 3.1 

Peskin and Schroeder book: Sec. 2.3

Notes: Lecture_5.pdf

 

Lecture 6. 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

Notes: Lecture_6.pdf

 

Lecture 7. 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

Notes: Lecture_7&8.pdf

 

Lecture 8. The quantised Dirac field

Peskin and Schroeder book: Secs. 3.5 

Mandl and Shaw book: Sec. 4.3

Notes: Lecture_7&8.pdf

 

Lecture 9. The quantised Dirac field

Peskin and Schroeder book: Sec. 3.6

Mandl and Shaw book: Sec. 4.4

Notes: Lecture_9.pdf

 

Lecture 10. Discrete symmetries 

Peskin and Schroeder book: Sec. 3.6

Notes: Lecture_10.pdf

 

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

Notes: Lecture_11.pdf

 

Lecture 12. Cross section and the S-matrix 

Peskin and Schroeder book: Sec. 4.5

Note: Lecture_12.pdf

 

Lecture 13. LSZ reduction formula: S-matrix elements from correlation functions

Peskin and Schroeder book: Secs. 7.1 and 7.2

Notes: Lecture_13&14.pdf

 

Lecture 14. Perturbative expansion and diagrammatic representation of correlation functions

Peskin and Schroeder book: Secs. 4.2, 4.3 and 4.4

Mandl and Shaw book: Sec. 6.3

Notes: Lecture_13&14.pdf

 

Lecture 15. Perturbative expansion and diagrammatic representation of S-matrix elements 

Peskin and Schroeder book: Secs. 4.6 and 7.2

Notes: Lecture_15.pdf

 

Lecture 16. Momentum space Feynman rules in QED 

Mandl and Shaw book: Secs. 7.1, 7.2, 7.3, 7.4, 8.3, 8.4 and 8.6

Peskin and Schroeder book: Secs. 4.7

Notes: Lecture_16.pdf

 

Lecture 17. Tree-level cross section calculations in QED

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

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

Notes: Lecture_17.pdf

 

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

Notes: Lecture_18.pdf

 

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

Notes: Lecture_19.pdf

 

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

Notes: Lecutre_20.pdf

 

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 three 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 20 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.