Groups of symmetry of quantum systems

Garant předmětu:

Jiří Tolar

Lecturer:

Jiří Tolar

Tutor:

Supervisor:

Department of Physics

Synopsis:

The lecture - preferably for the students of Mathematical Physics - is aimed to introduce them to advanced topics connected with applications of group theory in quantum physics. Starting with the Wigner theorem on symmetry operations in quantum physics, the classification of projective representations of Lie groups as well as the superselection rules will be dealt with. The groups important in physics – the Euclid, the Poincaré and the Galilei group – will be treated by Mackey’s method of induced representations.

Requirements:

Syllabus of lectures:

1.Wigner’s theorem, projective representations [2h]

2.Factor systems, central extenstions of groups, classification in terms of group cohomology [6h]

3.Superselection group [2h]

4.Induced representations of groups [4h]

5.Applications to the rotation, Euclid, Poincaré and Galilei groups [8h]

6.Quantum kinematics, the Heisenberg group, the Weyl-Wigner correspondence [4h]

Syllabus of tutorials:

Study Objective:

Study materials:

Povinná literatura:

[1] J. A. de Azcárraga, J. M. Izquierdo: Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics, (Cambridge University Press, Cambridge 1995)

[2] M. Hamermesh: Group Theory and Its Applications to Physical Problems , (Addison-Wesley, Reading, Mass.1964), kap. 12

Doporučená literatura:

[3] V. S. Varadarajan: Geometry of Quantum Theory, Vol. 2 Quantum Theory of Covariant Systems, (Van Nostrand Reinhold, New York 1970)

[4] D. J. Simms: Lie Groups and Quantum Mechanics, Lecture Notes in Mathematics, Vol. 52, (Springer-Verlag, Berlin 1968)

Note:

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans:

• Matematická fyzika (elective course)