LIOUVILLE EQUATION .5. THE FULL SYMMETRIES OF R(-1)-POTENTIALS

A systematic study of the symmetries of Liouville's equation for r-1-potential is presented. The canonical transformations in phase space which leave the hamiltonian invariant turn out to be the full symmetry transformations of Liouville's operator, as well. The symmetry group is SO(4). A maximal set of mutually commuting operators, and subsequently, a classification of the eigensolutions of Liouville operator is proposed. The Kustaanheimo-Stiefel transformation is used to show that this SO(4) is isomorphic to a constrained SU(4) and contains all symmetries of Liouville's equation for r-1-potential.