Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917769748938752 |
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| author | Padmanabhan, Pramod Korepin, Vladimir |
| author_facet | Padmanabhan, Pramod Korepin, Vladimir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11501 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras Padmanabhan, Pramod Korepin, Vladimir High Energy Physics - Theory Statistical Mechanics Mathematical Physics Quantum Physics 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. |
| title | Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2404.11501 |