LORENTZ TRANSFORMATIONS AS LIE-POISSON SYMMETRIES

We write down the Poisson structure for a relativistic particle where the Lorentz group does not act canonically, but instead as a Poisson-Lie group. In so doing we obtain. the classical limit of a particle moving on a noncommutative spaed possessing SL(q)(2, C) invariance. We show that if the standard mass shell constraint is chosen for the Hamiltonian function, then the particle interacts with the space-time. We solve for the particle trajectory and find that it originates and terminates at singularities. (C) 1995 American Institute of Physics.