2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/201527In this work it is proposed a transformation which is useful in order to simplify non-polynomial potentials given in the form of an exponential. As an application, it is shown that the quantum Liouville field theory may be mapped into a field theory with a polynomial interaction between two scalar fields and a massive vector field.15 pages, 4 figures, LaTeX + RevTeX 4. With respect to the previous version an appendix has been added to provide an alternative proof of Eq. (31). Title and abstract have been changedMathematical PhysicsStatistical MechanicsHigh Energy Physics - Theorytext