量子物理中的李代数

I. Kikuchi, Akihito Kikuchi
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引用次数: 1

摘要

本文介绍了如何将计算机代数包GAP(此http URL)应用于量子物理问题的计算中,其中李代数的应用是必不可少的。这篇文章包含了几个读者在台式电脑上可以遵循的示例计算:例如,李代数的基本思想的简要回顾,量子力学中的角动量,夸克八重路模型,以及Weyl特征公式的使用(为了构造权重模块,并正确计算简并)。这篇短文是对其中一位作者(A.K.)的文章“计算机代数和材料设计”[arXiv:1612.02275]的补充。后一篇文章也可以在arXiv中找到。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Lie algebra in quantum physics by means of computer algebra
This article explains how to apply the computer algebra package GAP (this http URL) 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.
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