Abstract:
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.
