N=2 Hamiltonians with sl(2) coalgebra symmetry and their integrable deformations

Details N=2 Hamiltonians with sl(2) coalgebra symmetry and their integrable deformations N=2 Hamiltonians with sl(2) coalgebra symmetry and their integrable deformations

1999-10-18

arxiv.org/abs/solv-int/9910009v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages Latex

Scientific paper

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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