Non-abelian Harmonic Oscillators and Chiral Theories

We show that a large class of physical theories which has been under intensive investigation recently, share the same geometric features in their Hamiltonian formulation. These dynamical systems range from harmonic oscillations to WZW-like models and to the KdV dynamics on DiffoS. To the same class belong also the Hamiltonian systems on groups of maps. The common feature of these models are the ’chiral’ equations of motion allowing for so-called chiral decomposition of the phase space. Onderzoeker I.I.K.W. Belgium, on leave from IFT University of Wroclaw, Poland On leave from IFT University of Wroclaw, Poland. Partially supported by KBN-grant 2 00 95 91 0