Quantum Field Theory 1

Relations:

In order to register for the course 02ZELW, the student must have successfully completed or received credit for and not exhausted all examination dates for the course 02KTPA1.

Course guarantor:

Martin Štefaňák

Lecturer:

Václav Zatloukal

Tutor:

Václav Zatloukal

Supervisor:

Department of Physics

Synopsis:

The lecture aims to introduce the students to both fundamental and applied parts of quantum field theory. The focus is in particular on equations of relativistic quantum mechanics, canonical quantization of scalar and bispinor field, perturbation theory (Feynman’s rules) and basics of renormalization. The content of the lecture can serve as a base for further study in fields of exactly solvable models, theory of critical phenomena, molecular chemistry and biochemistry or quantum gravity.

Requirements:

Syllabus of lectures:

1. Relativistic wave equations: Klein-Gordon’s equation, Dirac’s eqaution

2. Lorentz group and its representations, invariance of Dirac’s equation under proper Lorentz transformations,

bilinear forms

3. Solutions of Dirac’s equation for free particle, charged relativistic particle in an external electromagnetic field

4. Canonical quantization of a scalar field

5. Algebra of observables and particle interpretation

6. Canonical quantization of the Dirac’s field

7. Symetries and conservation laws, Noether’s theorem

8. Feynman’s propagator for a scalar and the Dirac’s field

9. Interacting fields, Wick’s theorem and perturbation theory

10. Scattering processes, S matrix and Feynman’s rules, cross-section, decay of an unstable particle

11. Renormalization of a φ4 theory

Syllabus of tutorials:

Solving problems to illustrate the theory from the lecture.

Study Objective:

Study materials:

Key references:

[1] C. Itzykson a J.-B. Zuber, Quantum Field Theory, Dover Publications, Inc., New York, 2005

[2] H. Kleinert, Particles and Quantum Fields, World Scientific, London, 2017

Recommended references:

[3] P. Ramond, Field Theory: A Modern Primer, Westview Press, London, 2001

[4] W. Greiner a J. Reinhard, Field Quantization, Springer, New York, 2012

Note:

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue	roomBR:10 Zatloukal V. 12:00–13:50 (lecture parallel1) Břehová 7
Wed	roomBR:114 Zatloukal V. 12:00–13:50 (lecture parallel1) Břehová 7
Thu	roomBR:114 Zatloukal V. 10:00–11:50 (parallel nr.101) Břehová 7
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Jaderná a částicová fyzika (compulsory course in the program)
• Matematická fyzika (compulsory course in the program)
• Kvantové technologie (compulsory course in the program)