Quantum Field Theory 2

Relations:

In order to register for the course 02ZQCD, the student must have successfully completed or received credit for and not exhausted all examination dates for the course 02KTPA2.

Course guarantor:

Martin Štefaňák

Lecturer:

Petr Jizba

Tutor:

Václav Zatloukal

Supervisor:

Department of Physics

Synopsis:

The lecture aims at introducing the students to the Feynmans functional integral and its applications. The focus is on broadening the knowledge of modern parts of relativistic and non-relativistic quantum field theory and statistical physics. 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. First quantization with path integral

2. Second quantization and functional integral, partition sum and Wicks theorem

3. Noethers theorem and anomalies

4. Perturbation expansion of Greens functions with Feynmans diagrams scalar field, generating functionals W

and Г

5. Grassmanns variables and Berezins functional integral for fermionic fields

6. Perturbation expansion of Greens functions with Feynmans diagrams fermionic fields, S-matrix and

LSZ formalism

7. Goldstones theorem and Higgs mechanism

8. Calibration fields and their quantization

9. Callan-Symanzik equation of renormalization group and β function

10. Some spectral properties of 2-point correlation functions

Syllabus of tutorials:

Solving problems to illustrate the theory from the lecture

Study Objective:

Study materials:

Key references:

[1] M. Blasone, P. Jizba and G. Vitiello, Quantum Field Theory and its Macroscopic Manifestations, Boson Condensation, Ordered Patterns and Topological Defects, Imperial College Press, London, 2011

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

Recommended references:

[3] E. Fradkin, Field Theories of Condensed Matter Physics, Cambridge University Press, New York, 2013

[4] A. Altland and B. Simons, Condensed Matter Field Theory, Cambridge University Press, Singapore, New York, 2013

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

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)