* Load is given in academic hour (1 academic hour = 45 minutes)
Goal is introducing students to elementary notions and methods of theory of Lie groups and their representations. Acquired knowledge and skills are then applied to concrete physical problems. Course complements and extends courses of quantum mechanics and enables deeper understanding of quantum mechanics itself, as well as later specialized courses (Nuclear physics and Physics of elementary particles).
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.3 apply standard methods of mathematical physics, in particular mathematical analysis and linear algebra and corresponding numerical methods
4. COMMUNICATION SKILLS
4.3 develop the written and oral English language communication skills that are essential for pursuing a career in physics
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
After successfully finishing the course, student will be able
1. to make distinction between finite and Lie groups
2. to understand connection between Lie algebras and Lie groups on examples of orthogonal and unitary groups occurring in applications in physics
3. to discuss familiar results in quantum theory of angular momentum using language of group theory
4. to describe structure of Lorentz group
1. Lie groups.
2. Examples of Lie groups important in physics.
3. Irreducible representations of group SO(2)
4. Irreducible representations of group SO(3)/SU(2)
5. Rotations and angular momentum in quantum mechanics
6. Addition of angular momenta and Clebsch-Gordan coefficients.
7. Tensor operators and Wigner-Eckart theorem. Applications.
8. Groups SU(2) and SU(3)
9. Groups SU(N) and Young tables
10. Lorentz transformations and group O(1,3)
11. Generators and representations of Lorentz group
12. Poincaré group. Conformal group.
REQUIREMENTS FOR STUDENTS:
Going to courses and doing homeworks.
GRADING AND ASSESSING THE WORK OF STUDENTS:
- K. Kumerički, Simetrije u fizici, skripte
- H. F. Jones, Groups, Representations and Physics, 2nd ed., IOP Publishing, 1998.
Introduction to Quantum Physics