Quantum Field Theory 3

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Physics

Synopsis:

The aim of the lecture is to familiarize the students with more advanced parts of Feynman's path and functional integral. The lecture focuses on deepening knowledge in modern passages of non-relativistic quantum field theory and statistical physics. The main focus is on applications in the condense matter theory and quantum optics. Material of teh lecture can also serve as a suitable basis for further study, e.g. in the field of exactly solvable systems, theory of critical phenomena, molecular chemistry and biochemistry.

Requirements:

02KTP1 (02KTPA1), 02KTP2 (02KTPA2)

Syllabus of lectures:

1. Feynman's path integral in quantum mechanics

3. WKB approximation using path integral

4. Non-perturbative methods in quantum theory (instantons, Bohm-Aharon effect, etc.)

5. Feynman path integral in holomorphic representation and coherent states. Weyl transform

6. Non-relativistic quantum field theory

7 Non-relativistic functional integral

8. Quantum field theory at finite temperatures

9. Applications in statistical quantum field theory and solid state theory

Syllabus of tutorials:

Solving problems to illustrate the theory from the lecture

Study Objective:

Knowledge:

To acquire advanced knowledge in applications of the path and functional integral of in quantum mechanics, statistical physics, quantum optics and non-relativistic quantum field theory (especially quantum condense matter theory).

Abilities:

Solving typical problems from advanced quantum mechanics, statistical physics, quantum optics and non-relativistic quantum field theory.

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

Recommended references:

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

[4] H. Kleinert, Particles and Quantum Fields, (World Scientific, London, 2017)

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Kvantové technologie (compulsory course in the program)