Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras

IF 2.5 3区 物理与天体物理 Q2 PHYSICS, PARTICLES & FIELDS Nuclear Physics B Pub Date : 2024-09-02 DOI:10.1016/j.nuclphysb.2024.116664
Pramod Padmanabhan , Vladimir Korepin
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Abstract

Bethe Ansatz was discovered in 1932. Half a century later its algebraic structure was unearthed: Yang-Baxter equation was discovered, as well as its multidimensional generalizations [tetrahedron equation and d-simplex equations]. Here we describe a universal method to solve these equations using Clifford algebras. The Yang-Baxter equation (d=2), Zamolodchikov's tetrahedron equation (d=3) and the Bazhanov-Stroganov equation (d=4) are special cases. Our solutions form a linear space. This helps us to include spectral parameters. Potential applications are discussed.

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利用克利福德代数方程求解杨-巴克斯特方程、四面体方程和高次单纯形方程
贝特公式发现于 1932 年。半个世纪后,它的代数结构被发掘出来:发现了杨-巴克斯特方程及其多维广义方程 [四面体方程和 d-复数方程]。在此,我们介绍一种利用克利福德代数求解这些方程的通用方法。杨-巴克斯特方程(d=2)、扎莫洛奇科夫四面体方程(d=3)和巴扎诺夫-斯特罗加诺夫方程(d=4)都是特例。我们的解形成了一个线性空间。这有助于我们纳入光谱参数。讨论了潜在的应用。
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来源期刊
Nuclear Physics B
Nuclear Physics B 物理-物理:粒子与场物理
CiteScore
5.50
自引率
7.10%
发文量
302
审稿时长
1 months
期刊介绍: Nuclear Physics B focuses on the domain of high energy physics, quantum field theory, statistical systems, and mathematical physics, and includes four main sections: high energy physics - phenomenology, high energy physics - theory, high energy physics - experiment, and quantum field theory, statistical systems, and mathematical physics. The emphasis is on original research papers (Frontiers Articles or Full Length Articles), but Review Articles are also welcome.
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