Group theory represents the mathematical language to deal with symmetry, since all transformations that leave a physical system invariant (usually described in terms of transformations of algebraic or differential equations) naturally form a group. Thus, arguments based on the symmetry of the considered system play a significant role within almost all branches of physics. Symmetry and symmetry breaking are basic concepts of nature. Furthermore, we give a complete list of the implemented commands including references for algorithms within the Supplementary Material. We illustrate the basic framework of the package and show basic examples to present the functionality. The package is designed to be easily accessible by providing a complete Mathematica-style documentation, an optional input validation and an error strategy. The content ranges from basic group theory and representation theory to more applied methods like crystal field theory, tight-binding and plane-wave approaches capable for symmetry based studies in the fields of solid-state physics and photonics.

We present the Mathematica group theory package GTPack providing about 200 additional modules to the standard Mathematica language.

2Institute of Physics, Martin Luther University Halle-Wittenberg, Halle, Germany.

1Nordita, KTH Royal Institute of Technology, Stockholm University, Stockholm, Sweden.

Matthias Geilhufe 1 * and Wolfram Hergert 2 *

Mathematica 11.3 direct download