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

Autor: Pramod Padmanabhan, Vladimir Korepin
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Nuclear Physics B, Vol 1007, Iss , Pp 116664- (2024)
Druh dokumentu: article
ISSN: 0550-3213
DOI: 10.1016/j.nuclphysb.2024.116664
Popis: 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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