Project Description

Symmetries in Quantum Mechanics and Particle Physics

In case that due to the Covid-19 pandemic an on-campus summerschool is not possible, this module will take place online.

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
  • Programme – The course is taught in English (4 ECTS)
  • Requirements – Students of mathematics and the natural sciences (physics, chemistry, biology) with introductory knowledge of Quantum Mechanics. Should be familiar with the Schrödinger equation, the concept of operators and commutation relations and standard methods of calculus.
  • Programme fee – tba. (includes all study materials, transcript of records, and health, liability and accident insurance as well as a public transportation ticket within Frankfurt).
  • Application deadline – tba.

Course description

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.

The course comprises 28 contact hours (8*3.5 hours). Upon successful completion, 4 ECTS (European Credit Transfer System) points will be awarded for the module. A single ECTS point is defined as the equivalent of 25 to 30 hours of student workload. This includes class hours, additional preparations for class activities, readings, assignments as well as final assessments. Assessment and award of credit points will be on a pass/fail basis, no grades will be given.

Attendance: Participants have to attend at least 80 % of the classes.

Requirements

The course aims at students of mathematics and the natural sciences (physics, chemistry, biology) who have taken an Introductory Quantum Mechanics course. They should be familiar with the Schrödinger equation, the concept of operators and commutation relations, as well as standard methods of calculus.

Instructors

Prof. Dr. Dirk H. Rischke (https://www.uni-frankfurt.de/65315388/AG-Rischke)

Florian Divotgey (https://itp.uni-frankfurt.de/~fdivotgey/)