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 space possessing SLq(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. copyright 1995 American Institute of Physics