CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Quantum Field Theory 1

Code Completion Credits Range
02KTPA1 Z,ZK 8 4P+2C
Vztahy:
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.
Garant předmětu:
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 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-08-15
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