Exactly Integrable Systems in Quantum Field Theory
Course: Quantum field theory
Structural unit: Faculty of Physics
Title
Exactly Integrable Systems in Quantum Field Theory
Code
ОК 11
Module type
Обов’язкова дисципліна для ОП
Educational cycle
Second
Year of study when the component is delivered
2021/2022
Semester/trimester when the component is delivered
2 Semester
Number of ECTS credits allocated
6
Learning outcomes
Know the method of transforming Bogolyubov to solve the two-dimensional Ising model.
Know the basic methods of conformal field theory.
Be able to apply the method of Bogolyubov transformations to the study of free-fermentary quantum systems.
Be able to find correlation functions in conformal field theory.
Form of study
Full-time form
Prerequisites and co-requisites
1. Know the basic methods of quantum field theory in operator formalism and formal integral integralism. Know the basic principles of statistical mechanics and the theory of phase transitions. Know the methods of group theory and their representations in applications to quantum physics.
2. Be able to apply previously acquired knowledge from the courses of mathematical analysis, theory of functions of complex variables, differential equations, mathematical physics, quantum mechanics, quantum field theory and statistical physics to solve practical problems.
3. To have basic skills of algebraic calculations in the course of linear algebra and analytical calculations in the course of the theory of functions of a complex variable.
Course content
1. Basic integrative models of statphysics and quantum theory.
2. Diagonalization of transfer matrices of the two-dimensional Ising model.
3. Magnetization in the Ising model.
4. Correlation functions in the Ising model.
5. Scaling limit of 2D Ising model.
6. Conformal symmetry in n-dimensional space.
7. Ward's identities in quantum field theory.
8. Conformal symmetry in 2-dimensional space.
9. Virasoro algebra as an algebra of symmetries in conformal field theory.
10. Multipoint correlation functions in conformal field theory.
11. Correlation functions with degenerate fields.
12. Bosonization.
Recommended or required reading and other learning resources/tools
1. N. Iorgov, O. Lisovyy, Ising correlations and elliptic determinants, https://arxiv.org/abs/1012.2856
2. P. Di Francesco, P. Mathieu, D. Sénéchal, Conformal Field Theory, Springer, 1997, 890 pp.
Planned learning activities and teaching methods
Lectures, practical classes, independent work.
Assessment methods and criteria
Modular test work, examination work.
Language of instruction
Ukrainian
Lecturers
This discipline is taught by the following teachers
Departments
The following departments are involved in teaching the above discipline