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