Infopaket

Group theory and symmetry

ОК3

Обов’язкова дисципліна для ОП

Second

2023/2024

1 Semester

3

Know: 1. basic principles of relativistic quantum mechanics and quantum field theory 2. basic principles of group theory 3. theory of representations 4. basics of Feynman charting technique 5. basic properties of unitary groups and their algebras Be2. find possible multiplicities of degeneracy of levels of quantum systems in the external field able to: 1. write Fenman diagrams for basic processes involving elementary particles 3. be able to decompose summary representations into irreducible components 4. to classify quantum systems in the external field

Full-time form

1. Know the basic principles of relativistic quantum mechanics and special relativity, the basics of Feynman's diagram technique, the basic principles and methods of group theory. 2. Be able to solve typical problems of relativistic quantum mechanics, calculate the scattering cross sections of the main processes of quantum electrodynamics, use the methods of group theory in the analysis of conservation laws and types of reactions. 3. Have the skills to study literature, work with interactive and multimedia tools, interact with colleagues during training.

Group theory and symmetry is a basic mathematical discipline in which students master the basic concepts and methods of group theory, learn to use system symmetry to obtain physical results, such as degeneracy and splitting of energy levels of quantum systems in fields with different symmetry, selection rules, classification elementary particles in models with different types of symmetry, study of the physical properties of hadrons (masses, magnetic moments, etc.).

Basic: 1.Khamermesh M. Group theory and its application to physical problems. - 1966. - 588 p. 2.Landau L.D., Lifshitz O.M. Quantum Mechanics, Volume 3, Chapter 8 - Symmetry Theory. 1989. Additional: 1.Greiner W., Reinhart J. Quantum elektrodynamics.Springer, 2003. 2.Lyubarsky G.Ya. Group theory and its application in physics. 4th type 1968. - 268 p.. 3.Weinberg S. Quantum field theory. T.1. General theory. 2003. – 648 p.

Lecture demonstration; individual work; consultations

The final assessment in the form of a test is carried out in the form of an oral interview and a written solution of the proposed tasks. The total number of points for the test is 40 points (20 + 4 + 6 + 10). The test ticket includes two theoretical questions and two practical ones. The grade for written work is entered in the record only if it is equal to or greater than 24 points (i.e. from 34 to 40). If the overall grade for written work is less than 24 points, then 0 points are entered in the test sheet and the test is simple and the overall grade for the discipline is "unsatisfactory".

Ukrainian