dorsal/arxiv
View SchemaA systematic construction of completely integrable Hamiltonians from coalgebras
| Authors | Angel Ballesteros, Orlando Ragnisco |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9802008 |
| URL | https://arxiv.org/abs/solv-int/9802008 |
| DOI | 10.1088/0305-4470/31/16/009 |
Abstract
A universal algorithm to construct N-particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum deformations can be interpreted as generating structures for integrable deformations of Hamiltonian systems with coalgebra symmetry. In order to illustrate this general method, the $so(2,1)$ algebra and the oscillator algebra $h_4$ are used to derive new classical integrable systems including a generalization of Gaudin-Calogero systems and oscillator chains. Quantum deformations are then used to obtain some explicit integrable deformations of the previous long-range interacting systems and a (non-coboundary) deformation of the $(1+1)$ Poincar\'e algebra is shown to provide a new Ruijsenaars-Schneider-like Hamiltonian.
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"abstract": "A universal algorithm to construct N-particle (classical and quantum)\ncompletely integrable Hamiltonian systems from representations of coalgebras\nwith Casimir element is presented. In particular, this construction shows that\nquantum deformations can be interpreted as generating structures for integrable\ndeformations of Hamiltonian systems with coalgebra symmetry. In order to\nillustrate this general method, the $so(2,1)$ algebra and the oscillator\nalgebra $h_4$ are used to derive new classical integrable systems including a\ngeneralization of Gaudin-Calogero systems and oscillator chains. Quantum\ndeformations are then used to obtain some explicit integrable deformations of\nthe previous long-range interacting systems and a (non-coboundary) deformation\nof the $(1+1)$ Poincar\\\u0027e algebra is shown to provide a new\nRuijsenaars-Schneider-like Hamiltonian.",
"arxiv_id": "solv-int/9802008",
"authors": [
"Angel Ballesteros",
"Orlando Ragnisco"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1088/0305-4470/31/16/009",
"title": "A systematic construction of completely integrable Hamiltonians from coalgebras",
"url": "https://arxiv.org/abs/solv-int/9802008"
},
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