dorsal/arxiv
View SchemaN=2 Hamiltonians with sl(2) coalgebra symmetry and their integrable deformations
| Authors | A. Ballesteros, O. Ragnisco |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9910009 |
| URL | https://arxiv.org/abs/solv-int/9910009 |
Abstract
Two dimensional classical integrable systems and different integrable deformations for them are derived from phase space realizations of classical $sl(2)$ Poisson coalgebras and their $q-$deformed analogues. Generalizations of Morse, oscillator and centrifugal potentials are obtained. The N=2 Calogero system is shown to be $sl(2)$ coalgebra invariant and the well-known Jordan-Schwinger realization can be also derived from a (non-coassociative) coproduct on $sl(2)$. The Gaudin Hamiltonian associated to such Jordan-Schwinger construction is presented. Through these examples, it can be clearly appreciated how the coalgebra symmetry of a hamiltonian system allows a straightforward construction of different integrable deformations for it.
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"date_created": "2026-03-02T18:02:51.573000Z",
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"abstract": "Two dimensional classical integrable systems and different integrable\ndeformations for them are derived from phase space realizations of classical\n$sl(2)$ Poisson coalgebras and their $q-$deformed analogues. Generalizations of\nMorse, oscillator and centrifugal potentials are obtained. The N=2 Calogero\nsystem is shown to be $sl(2)$ coalgebra invariant and the well-known\nJordan-Schwinger realization can be also derived from a (non-coassociative)\ncoproduct on $sl(2)$. The Gaudin Hamiltonian associated to such\nJordan-Schwinger construction is presented. Through these examples, it can be\nclearly appreciated how the coalgebra symmetry of a hamiltonian system allows a\nstraightforward construction of different integrable deformations for it.",
"arxiv_id": "solv-int/9910009",
"authors": [
"A. Ballesteros",
"O. Ragnisco"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "N=2 Hamiltonians with sl(2) coalgebra symmetry and their integrable deformations",
"url": "https://arxiv.org/abs/solv-int/9910009"
},
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