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arXiv · 2409.18489

Lie-Hamilton systems associated with the symplectic Lie algebra $\mathfrak{sp}(6, \mathbb{R})$

O. Carballal·R. Campoamor-Stursberg·F. J. Herranz
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Abstract

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

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O. Carballal, R. Campoamor-Stursberg, F. J. Herranz. 2024-09-27. Lie-Hamilton systems associated with the symplectic Lie algebra $\mathfrak{sp}(6, \mathbb{R})$. https://doi.org/10.7546/jgsp-69-2024-37-57

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