Spin and gauge models in lattice field theory
Course: Quantum field theory
Structural unit: Faculty of Physics
Title
Spin and gauge models in lattice field theory
Code
ОК 9
Module type
Обов’язкова дисципліна для ОП
Educational cycle
Second
Year of study when the component is delivered
2023/2024
Semester/trimester when the component is delivered
2 Semester
Number of ECTS credits allocated
3
Learning outcomes
Know the main properties of spin models with ferromagnetic interaction and perturbative lattice theory.
Know the calibration theories on the lattice and their properties, three-dimensional Abelian calibration theories, and the basics of non-Abelian calibration theories.
Be able to calculate the mass gap for Abelian and non-Abelian models and perturbative calculation of free energy.
Be able to solve two-dimensional calibration theories.
Form of study
Full-time form
Prerequisites and co-requisites
1. Know statistical mechanics, basic principles of calibration theories, critical theory phenomena and phase transitions, perturbative quantum field theory.
2. Be able to apply methods of asymptotic decompositions of multidimensional integrals.
Course content
1. Introduction to the lattice model.
2. Methods of plasma description Properties of spin models with ferromagnetic interaction. One-dimensional spin models.
3. Two-dimensional XY-model.
4. Perturbative theory on the lattice.
5. Two-dimensional non-Abelian models.
6. Calibration theories on the lattice and their properties.
7. Solving two-dimensional calibration theories.
8. Three-dimensional Abelian calibration theories. Fundamentals of non-Abelian calibration theories.
Recommended or required reading and other learning resources/tools
1. C. Itzykson, J. M.Drouffe. Statistical field theory. Volume 1 and 2, Cambridge University
Press, 2012.
2. J. Kogut. An introduction to lattice gauge theory and spin systems, Rev.Mod.Phys. -1979.
-Volume 51, No4. -P.659-713.
3. H. J. Rothe, Lattice Gauge Theories: An Introduction, World Scientific Publishing
Company; 4th edition., 2012.
Planned learning activities and teaching methods
Lectures, practical classes, independent work.
Assessment methods and criteria
Current survey, modular test, test 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