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Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras (2404.11501v2)
Published 17 Apr 2024 in hep-th, cond-mat.stat-mech, math-ph, math.MP, and quant-ph
Abstract: Bethe Ansatz was discoverd 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 ($d=2$), Zamalodchikov'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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