Course syllabus

Course-PM

FUF020 FUF020 Quantum field theory lp4 VT24 (7.5 hp)

Course is offered by the department of Physics

Contact details

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

Student representatives: 

Emil Babayev;   aebabayev@gmail.com     
Simon Dovrén;   simon.dovren@gmail.com  
Lise Hanebring;   lise.hanebring@gmail.com        
Jacob Ljungberg;   Jacoblju@student.chalmers.se    
Johanna Örgård;   johanna.orgard@gmail.com        

 

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

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

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

4) My lecture notes (uploaded on Canvas). 

 

Course design

The course is organised in blackboard lectures of 1h and 45 min each, including a 15 minute-long break.

The physics content of the course is described in detail below, and summarised in 19 thematic pdf lecture notes. 

These 19 themes will be covered in  24 in-person lectures.

In order to pass this course, you will have to take an oral exam and solve three problem sets. Further details on the structure of the exam can be found at the end of this webpage, in the examination form section.

The problem sets will be distributed through Canvas' assignments built-in function.

 

Lecture notes 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 notes 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 notes 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 Download Lecture_3.pdf

 

Lecture notes 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.pdfDownload Lecture_4.pdf

 

Lecture notes 5. The quantised real Klein-Gordon field

Mandl and Shaw book: Sec. 3.1 

Peskin and Schroeder book: Sec. 2.3

Notes: Lecture_5.pdfDownload Lecture_5.pdf

 

Lecture notes 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.pdfDownload Lecture_6.pdf

 

Lecture notes 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.pdfDownload Lecture_7&8.pdf

 

Lecture notes 8. The quantised Dirac field

Peskin and Schroeder book: Secs. 3.5 

Mandl and Shaw book: Sec. 4.3

Notes: Lecture_7&8.pdfDownload Lecture_7&8.pdf

 

Lecture notes 9. The quantised Dirac field

Peskin and Schroeder book: Sec. 3.6

Mandl and Shaw book: Sec. 4.4

Notes: Lecture_9.pdfDownload Lecture_9.pdf

 

Lecture notes 10. Discrete symmetries 

Peskin and Schroeder book: Sec. 3.6

Notes: Lecture_10.pdfDownload Lecture_10.pdf

 

Lecture notes 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.pdfDownload Lecture_11.pdf

 

Lecture notes 12. Cross section and the S-matrix 

Peskin and Schroeder book: Sec. 4.5

Note: Lecture_12.pdfDownload Lecture_12.pdf

 

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

Peskin and Schroeder book: Secs. 7.1 and 7.2

Notes: Lecture_13&14.pdfDownload Lecture_13&14.pdf

 

Lecture notes 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.pdfDownload Lecture_13&14.pdf

 

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

Peskin and Schroeder book: Secs. 4.6 and 7.2

Notes: Lecture_15.pdfDownload Lecture_15.pdf

 

Lecture notes 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.pdfDownload Lecture_16.pdf

 

Lecture notes 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.pdfDownload Lecture_17.pdf

 

Lecture notes 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.pdfDownload Lecture_18.pdf

 

Lecture notes 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.pdfDownload Lecture_19.pdf

 

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

Notes: Lecutre_20.pdfDownload 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.