$p$-adic angular momentum coupling in symplectic geometry
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909847621992448 |
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| author | Crespo, Luis Pelayo, Álvaro |
| author_facet | Crespo, Luis Pelayo, Álvaro |
| contents | The coupled angular momentum is an integrable system with two degrees of freedom which is fundamental in physics and the theory of integrable systems. It is obtained by coupling two angular momenta. We construct a $p$-adic analog of this system for any prime number $p$ and describe its symplectic normal forms at the critical points. This analog has a rich singularity theory with up to thirteen non-equivalent symplectic normal forms, which stands in contrast with the real case where there are exactly three normal forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13415 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $p$-adic angular momentum coupling in symplectic geometry Crespo, Luis Pelayo, Álvaro Symplectic Geometry Mathematical Physics 53D20, 37P05 The coupled angular momentum is an integrable system with two degrees of freedom which is fundamental in physics and the theory of integrable systems. It is obtained by coupling two angular momenta. We construct a $p$-adic analog of this system for any prime number $p$ and describe its symplectic normal forms at the critical points. This analog has a rich singularity theory with up to thirteen non-equivalent symplectic normal forms, which stands in contrast with the real case where there are exactly three normal forms. |
| title | $p$-adic angular momentum coupling in symplectic geometry |
| topic | Symplectic Geometry Mathematical Physics 53D20, 37P05 |
| url | https://arxiv.org/abs/2510.13415 |