Group Theory in Physics An Introduction with a Focus on Solid State Physics

This textbook provides a didactic introduction to the topic of group theory in physics, with a special focus on solid state physics issues. The book is useful for students who encounter such problems in their first scientific work (in theory or experiment). In addition to the basic introduction to group theory and representation theory, the book deals with point groups, double point groups, and space groups, which are essential in solid state physics. As an example for systems with space group symmetry, electrons in periodic potentials are discussed.

Furthermore, there are chapters on material tensors and the Wigner Eckart theorem for the evaluation of matrix elements. The latter is especially interesting for students dealing with spectroscopic problems. The content is accompanied by a series of exercises and examples. A set of solutions can be found in the appendix.

Introduction.- Groups: Definitions and Properties.- Point Groups.- Representations and Characters.- Orthogonality Theorems.- Quantum Mechanics and Group Theory.- Irreducible Representations of the Point Groups in Solids.- Group Theory in Stationary Perturbation Theory Calculations.- Material Tensors and Tensor Operators.- Matrix Elements of Tensor Operators: The Wigner-Eckart Theorem.- Double Groups and their Representations.- Space Groups.- Representations of Space Groups.- Particles in Periodic Potentials.

After completing his doctorate in theoretical physics at the University of Dortmund in 1998, he taught and researched at the universities of Marburg, Oxford, Cottbus and Hanover. His main area of research is correlated electron systems, in particular the physics of multi-band Hubbard models.

He came into contact with the problems of group theory in solid-state physics at an early stage and his first lecture on the subject he gave in Marburg in 2015. After that, he gave the lecture several times at the universities in Cottbus and Dortmund. Since 2017, he has a permanent position as a lecturer at TU Dortmund.