Symmetries in Quantum Mechanics and Particle Physics (02-13 Aug.)

Module content

  • Learn about group-theoretical methods that are frequently used in the framework of quantum mechanics and particle physics
  • Develop the basic notions of group theory and study Lie groups
  • Study Lie group of special unitary transformations and discuss its relevance for the theory of the strong interaction
  • Investigate the properties of the Poincaré group, which is the Lie group of symmetries of Minkowski space-time

Symmetry is an important concept in modern physics. It is at the heart of the fundamental forces of Nature, allows to discover connections between seemingly unrelated phenomena, and provides an ordering principle to classify experimental observations. The mathematical tool to describe symmetries is group theory.

In this module, we introduce the group-theoretical methods that are frequently used in the framework of quantum mechanics and particle physics, and discuss pertaining applications. After an introductory discussion of the quantum-mechanical realization of energy, momentum, and angular-momentum conservation, we develop the basic notions of group theory and study Lie groups, their properties, and respective representations. As the most important example for applications in particle physics, we introduce the Lie group of special unitary transformations and discuss its relevance for the theory of the strong interaction. Finally, as a second example of wide-reaching importance, we investigate the properties of the Poincaré group, which is the Lie group of symmetries of Minkowski space-time.