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 Feynman’s 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 Wick’s theorem

3. Noether’s theorem and anomalies

4. Perturbation expansion of Green’s functions with Feynman’s diagrams – scalar field, generating functionals W

and Г

5. Grassmann’s variables and Berezin’s functional integral for fermionic fields

6. Perturbation expansion of Green’s functions with Feynman’s diagrams – fermionic fields, S-matrix and

LSZ formalism

7. Goldstone’s 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)