Lie-Hamilton systems associated with the symplectic Lie algebra $\mathfrak{sp}(6, \mathbb{R})$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910771870433280 |
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| author | Carballal, O. Campoamor-Stursberg, R. Herranz, F. J. |
| author_facet | Carballal, O. Campoamor-Stursberg, R. Herranz, F. J. |
| contents | New classes of Lie-Hamilton systems are obtained from the six-dimensional fundamental representation of the symplectic Lie algebra $\mathfrak{sp}(6,\mathbb{R})$. The ansatz is based on a recently proposed procedure for constructing higher-dimensional Lie-Hamilton systems through the representation theory of Lie algebras. As applications of the procedure, we study a time-dependent electromagnetic field and several types of coupled oscillators. The irreducible embedding of the special unitary Lie algebra $\mathfrak{su}(3)$ into $\mathfrak{sp}(6, \mathbb{R})$ is also considered, yielding Lie-Hamilton systems arising from the sum of the quark and antiquark three-dimensional representations of $\mathfrak{su}(3)$, which are applied in the construction of t-dependent coupled systems. In addition, t-independent constants of the motion are obtained explicitly for all these Lie-Hamilton systems, which allows the derivation of a nonlinear superposition rule |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18489 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lie-Hamilton systems associated with the symplectic Lie algebra $\mathfrak{sp}(6, \mathbb{R})$ Carballal, O. Campoamor-Stursberg, R. Herranz, F. J. Mathematical Physics Dynamical Systems Exactly Solvable and Integrable Systems 17B10, 34A26, 34C14, 58A30 New classes of Lie-Hamilton systems are obtained from the six-dimensional fundamental representation of the symplectic Lie algebra $\mathfrak{sp}(6,\mathbb{R})$. The ansatz is based on a recently proposed procedure for constructing higher-dimensional Lie-Hamilton systems through the representation theory of Lie algebras. As applications of the procedure, we study a time-dependent electromagnetic field and several types of coupled oscillators. The irreducible embedding of the special unitary Lie algebra $\mathfrak{su}(3)$ into $\mathfrak{sp}(6, \mathbb{R})$ is also considered, yielding Lie-Hamilton systems arising from the sum of the quark and antiquark three-dimensional representations of $\mathfrak{su}(3)$, which are applied in the construction of t-dependent coupled systems. In addition, t-independent constants of the motion are obtained explicitly for all these Lie-Hamilton systems, which allows the derivation of a nonlinear superposition rule |
| title | Lie-Hamilton systems associated with the symplectic Lie algebra $\mathfrak{sp}(6, \mathbb{R})$ |
| topic | Mathematical Physics Dynamical Systems Exactly Solvable and Integrable Systems 17B10, 34A26, 34C14, 58A30 |
| url | https://arxiv.org/abs/2409.18489 |