A relativistic particle in the Liouville field

We investigate a model for a relativistic particle in the Liouville field. The model is $SL(2,R)/Z_2$ invariant. The corresponding dynamic integrals describe the whole set of classical trajectories. These integrals are used for the gauge-invariant Hamiltonian reduction. We propose a new scheme for quantizing the reduced system. The quantum system obtained reproduces the classical symmetry. We discuss the physical aspects of the model.