Lie algebra in quantum physics by means of computer algebra

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Kikuchi, Ichio ; Kikuchi, Akihito (2017)
  • Subject: Mathematics - Rings and Algebras | High Energy Physics - Theory | Physics - Computational Physics

This article explains how to apply the computer algebra package GAP ( 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.
  • References (4)

    [1] Akihito Kikuchi, \Computational Algebra and Material Design", arXiv:1612.02275, 2016.

    [2] \GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra",

    [3] Nathan Jacobson,\Lie Algebras", Dover Books on mathematics.

    [4] James E. Humphreys,\Introduction to Lie Algebras and Representation Theory", Springer-Verlag, 1980.

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