三元 $$Z_3$$ - 对称代数和广义量子振荡器

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-02-01 DOI:10.1134/s0040577924010070

R. Kerner

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引用次数: 0

摘要

摘要我们提出了一个用三元海森堡代数描述的量子振荡器的广义版本。该模型引出了一个六阶哈密顿，其能级可以用玻尔-索默费尔德量子化程序离散化。我们注意到它与应用于夸克颜色动力学的狄拉克方程的（Z_3\）扩展版本有相似之处，后者也会导致六阶场方程。论文还包含了对$Z_3$级结构（包括三元代数）的全面指导，这构成了所建议的泛化的数学基础。论文还讨论了模型的对称性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Ternary $$Z_3$$ -symmetric algebra and generalized quantum oscillators

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Ternary $$Z_3$$ -symmetric algebra and generalized quantum oscillators

Abstract

We present a generalized version of a quantum oscillator described by means of a ternary Heisenberg algebra. The model leads to a sixth-order Hamiltonian whose energy levels can be discretized using the Bohr–Sommerfeld quantization procedure. We note the similarity with the $Z_3$-extended version of Dirac’s equation applied to quark color dynamics, which also leads to sixth-order field equations. The paper also contains a comprehensive guide to $Z_3$-graded structures, including ternary algebras, which form a mathematical basis for the proposed generalization. The symmetry properties of the model are also discussed.

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.