Ren-integrable and ren-symmetric integrable systems
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909214208688128 |
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| author | Lou, S. Y. |
| author_facet | Lou, S. Y. |
| contents | A new type of symmetry, ren-symmetry describing anyon physics and the corresponding topological physics, is proposed. Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such as the super-symmetric quantum mechanics, super-symmetric gravity, super-symmetric string theory, super-symmetric integrable systems and so on. The super-symmetry and Grassmann-number are, in some sense, the dual conceptions, which turns out that these conceptions coincide for the ren situation, that is, a similar conception of ren-number is devised to ren-symmetry. In particular, some basic results of the ren-number and ren-symmetry are exposed which allow one to derive, in principle, some new types of integrable systems including ren-integrable models and ren-symmetric integrable systems. Training examples of ren-integrable KdV type systems and ren-symmetric KdV equations are explicitly given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_12388 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ren-integrable and ren-symmetric integrable systems Lou, S. Y. Exactly Solvable and Integrable Systems Mathematical Physics Pattern Formation and Solitons A new type of symmetry, ren-symmetry describing anyon physics and the corresponding topological physics, is proposed. Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such as the super-symmetric quantum mechanics, super-symmetric gravity, super-symmetric string theory, super-symmetric integrable systems and so on. The super-symmetry and Grassmann-number are, in some sense, the dual conceptions, which turns out that these conceptions coincide for the ren situation, that is, a similar conception of ren-number is devised to ren-symmetry. In particular, some basic results of the ren-number and ren-symmetry are exposed which allow one to derive, in principle, some new types of integrable systems including ren-integrable models and ren-symmetric integrable systems. Training examples of ren-integrable KdV type systems and ren-symmetric KdV equations are explicitly given. |
| title | Ren-integrable and ren-symmetric integrable systems |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2305.12388 |