关于 N=1 超对称鲁伊塞纳尔斯-施耐德三体模型可整性的评论

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-03-14 DOI:arxiv-2403.09204

Anton Galajinsky

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引用次数: 0

摘要

证明了基于势W(x)=2/x、W(x)=2/sin(x)和W(x)=2/sinh(x)的N=1超对称Ruijsenaars-Schneider三体模型的积分性。构建一组可代数解析的格拉斯曼-多运动常数的问题被简化为寻找一个向量三元组，使得它们的所有标量积都可以用原来的玻色初积分来表示。超对称泛化被用来建立各自的鲁伊塞纳斯-施耐德三体系统的新颖可积分（等）自旋扩展。

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Remarks on integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models

Integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models based upon the potentials W(x)=2/x, W(x)=2/sin(x), and W(x)=2/sinh(x) is proven. The problem of constructing an algebraically resolvable set of Grassmann-odd constants of motion is reduced to finding a triplet of vectors such that all their scalar products can be expressed in terms of the original bosonic first integrals. The supersymmetric generalizations are used to build novel integrable (iso)spin extensions of the respective Ruijsenaars-Schneider three-body systems.

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arXiv - PHYS - Exactly Solvable and Integrable Systems

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