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We investigate a model for a relativistic particle in the Liouville field. The model is SL(2, R)/Z2 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.

A relativistic particle in the liouville field