Clifford Solver for the Tetrahedron Equation and its Variants
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912673773387776 |
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| author | Padmanabhan, Pramod Singh, Vivek Kumar Korepin, Vladimir |
| author_facet | Padmanabhan, Pramod Singh, Vivek Kumar Korepin, Vladimir |
| contents | The different forms of the tetrahedron equation appear when all possible ways to label the scattering process of infinitely long straight lines are considered in three dimensional spacetime. This is expected to lead to three dimensional integrability, analogous to the Yang-Baxter equation. Among the three possibilities, we consider two of them and their variants. We show that Clifford algebras solve both the constant and the spectral parameter dependent versions of all of them. We also present a scheme for canonically solving higher simplex equations using tetrahedron solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Clifford Solver for the Tetrahedron Equation and its Variants Padmanabhan, Pramod Singh, Vivek Kumar Korepin, Vladimir High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems The different forms of the tetrahedron equation appear when all possible ways to label the scattering process of infinitely long straight lines are considered in three dimensional spacetime. This is expected to lead to three dimensional integrability, analogous to the Yang-Baxter equation. Among the three possibilities, we consider two of them and their variants. We show that Clifford algebras solve both the constant and the spectral parameter dependent versions of all of them. We also present a scheme for canonically solving higher simplex equations using tetrahedron solutions. |
| title | Clifford Solver for the Tetrahedron Equation and its Variants |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2510.23944 |