Lecturer: Prof. Dr. Yakov Shnir, University of Minsk

Description:

The course aims at giving a self-contained introduction to the modern technique of quantization in different physical contexts. An approach emphasising the simplest models is used, progressing to discussion of real systems before mentioning more general and rigorous conclusions. The course is structured around carefully selected problems, which are solved in detail. The central concept is that of effective action (or free energy in statistical physics), and the main technical tool is the path integral,
although other formalisms are also mentioned. The course is based on the original textbooks

1. V.G. Kiselev, Ya.M. Shnir and A.Ya. Tregubovich - Introduction to Quantum Field Theory", Taylor & Francis, UK, 2000
2. Ya M Shnir - Topological and Non-Topological Solitons; Cambridge University Press, Cambridge Monographs in Mathematical Physics, UK, 2018

The lecture course will cover

1. Technique of functional integration in Quantum Mechanics and in Quantum Field Theory.
2. Quantum mechanical instantons, double well problem.
3. Effective potential of the ϕ4 theory.
4. Regularization and renormalization. Running coupling constant, renormalization group equations. Anomalies.
5. Effective action of ϕ4 theory.
6. Functional integration over fermions.
7. Functional integration in gauge theories.
8. Coleman-Weinberg effect.
9. Non-perturbative phenomena in field theory. Kinks and vortices.
10. Monopoles and instantons.