# Group Theory

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### Group Theory

 Code: 63019 ECTS: 4.0 Lecturers in charge: doc. dr. sc. Sanjin Benić - Lectures Lecturers: Sanjin Benić - Exercises Take exam: Studomat

### 1. komponenta

Lecture typeTotal
Lectures 30
Exercises 15
Description:
COURSE GOALS:
Goal is introducing students to elementary notions and methods of theory of 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 (Physics of condensed matter, 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 define notions of groups and group representations and give simple finite group examples
2. make distinction between finite, infinite and Lie groups
3. make distinction between reducible and irreducible group representations in definition and in concrete examples of finite groups
4. make explicit reduction of reducible representations of crystallographic groups to direct sum of irreducible ones

COURSE DESCRIPTION:
1. Groups. Crystallographic point groups.
2. Subgroups. Homomorphism and isomorphism of groups.
3. Group representations. Equivalence of representations.
4. Sum and product of representations. Reducibility.
5. Schur lemmas and orthogonality relations
6. Character tables. Decomposition of reducible representations.
7. Applications: Dipole moments of crystals. Degeneracy and level splitting.
8. Symmetries in classical and quantum mechanics. Transformations and conservation laws. Tensors.
9. Space transformations of quantum systems.
10. Bloch theorem. Spin.
11. Lie groups.
12. Lie algebras.

REQUIREMENTS FOR STUDENTS:
Going to courses and doing homeworks.

GRADING AND ASSESSING THE WORK OF STUDENTS:
Literature:
1. H. F. Jones, Groups, Representations and Physics, 2nd ed., IOP Publishing, 1998.
2. K. Kumerički, Grupe, simetrije i tenzori u fizici, online skripte http://www.phy.pmf.unizg.hr/~kkumer/articles.html#teaching
Prerequisit for:
Enrollment :
Passed : Introduction to Quantum Physics
Passed : Linear Algebra 2
 5. semester Izborni predmet - Mandatory studij - Physics 6. semester Not active Izborni predmet - Mandatory studij - Physics
Consultations schedule:

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