Lie algebra in quantum physics by means of computer algebra

TL;DR

This paper demonstrates how to use the GAP computer algebra system to perform Lie algebra computations relevant to quantum physics, including angular momentum, quark models, and Weyl character formulas, with practical examples.

Contribution

It provides a practical guide for applying GAP to Lie algebra problems in quantum physics, with illustrative computations and explanations.

Findings

Successful implementation of Lie algebra calculations in quantum physics using GAP

Examples include angular momentum, quark models, and Weyl character formulas

Facilitates computational approaches for physicists using computer algebra systems

Abstract

This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold way model, and the usage of Weyl character formula (in order to construct weight modules, and to count correctly the degeneracy). This short article is a complement to the article "Computer Algebra and Material Design" [arXiv:1612.02275] by one of the authors (A.K.). The latter article is also available in the arXiv.