2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55094A model of a relativistic particle moving in the Liouville field is investigated. Symmetry group of the system is $SL(2,R)/Z_2$. The corresponding dynamical integrals describe full set of classical trajectories. Dynamical integrals are used for the gauge-invariant Hamiltonian reduction. The new scheme is proposed for quantization of the reduced system. Obtained quantum system reproduces classical symmetry. Physical aspects of the model are discussed.17 pages, Latex, no figuresHigh Energy Physics - Theorytext