Théorie des Champs Quantiques 1
Topic outline
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University: Djilali Bounaama Khemis Miliana
Faculty: Science of Matter and Computer Science
Department: physics
Speciality: theoretical physics
Level: Master 1
Module: Quantum Field Theory I
Semester:1
Credit: 06
Unit: Fundamental.
Coefficient: 3.
Timetable: 1h30 min, 3 sessions per week (2 lectures and 1 TD)
Teacher responsible for the course: Dr. FERMOUS Rachid.
Grade: MCA
Assessment method:
The final assessment is carried out through:
- Assessment of tutorials: which represents 50% (12 points for presentations, 5 points for attendance and 3 points for participation).
- A table-top final exam: which accounts for 50% of the final mark, and which covers everything you have seen in this course during the semester.
To pass. -
To pass the module, you must have an overall average of at least 10 out of 20.
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- Understand the concept of canonical quantization for scalar fields, vector fields, and fermion fields.
- Understand the concept of global and local symmetry in quantum field theory and their implications.
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Quantum mechanics, analytical mechanics, electromagnetism, special relativity
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1 Preface 3
2 A review of quantum mechanics 4
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . 4
2.2 Wave modeling . . . . . . . . . . . . . . . . . . 4
2.3 Schrödinger equation . . . . . . . . . . . 5
2.4 Harmonic oscillator . . . . . . . . . . . . . . 6
2.5 Pauli equation . . . . . . . . . . . . . . . . . 6
3 Exercises 7
4 A review of special relativity 8
4.1 Overview of the laws of electromagnetism . . . . 8
4.1.1 Maxwell equations . . . . . . . . . 8
4.1.2 Vector and scalar potentials . . . . . . .10
4.2 Vector analysis in Minkowski space . . . 11
4.2.1 Quadri-divergence and quadri-gradient . . 11
4.2.2 Quad-vector current density . . . . .12
4.2.3 Quad-vector potential . . . .13
4.2.4 Electromagnetic field tensor . . . . .13
4.2.5 Change of variable . . . . . .15
5 Exercises6 Symmetry and invariance 19
6.1 Definition . . . . . .19
6.2 Types of transformations . . . 19
6.2.1 Geometric transformations . . . . 19
6.2.2 Internal transformations . . . . 20
6.2.3 Internal geometric transformations . . .20
7 Exercises8 Klein-Gordon equation 22
8.1 Introduction . . . . . . . . . . . 22
8.2 Quadri-vectors in field theory. . . . 23
8.3 Free Klein-Gordon equation . . . . .24
8.4 Invariance of the free Klein-Gordon equation under gauge transformation . . . 26
8.5 Solutions to the free Klein-Gordon equation . . 26
8.6 Physical interpretation of solutions to the free Klein-Gordon equation . . . . . 28
9 Klein-Gordon equation in the presence of an external electromagnetic field 30
9.1 invariance of the Klein-Gordon equation under the presence of an external electromagnetic field through gauge transformation . . . .31
9.2 Klein-Gordon equation current in the presence of an external electromagnetic field 31
10 Exercises 33
11 Somme References 35 -
1. J. P. Derendinger, Théorie quantique des champs, Presses polytechnique et universitaires
romandes, 2001
2. S. Weinberg, Quantum theory of fields, 3 vols, Cambridge University Press, 1995,1996
3. J. J. Sakurai, Advanced quantum rnechanics, Addison-Wesley, 1967
4. J. D. Bjorken and S.D. Drell, Relativistic quantum fields, McGraw-Hill, 1965
5. F. Mandl et G.Shaw., Quantum field theory, Addison-Wesley, 1993
6. N. N. Bogoliubov, D. V. Shirkov, Introduction to the Theory of Quantized Fields (Interscience
Monographs in Physics and Astronomy), John Wiley & Sons, 1959
7. R. Balian, du microscopique au macroscopique, vol. 2. École polytechnique, ellipses, 1982
