On the S-matrix of Liouville theory

A bstract The S -matrix for each chiral sector of Liouville theory on a cylinder is computed from the loop expansion correlation functions one-dimensional field circle with non-local kinetic energy and an exponential potential. This action Legendre transform generating function semiclassical scattering amplitudes. It derived relation between asymptotic in - out -fields. Its relevance quantum process demonstrated by comparing explicit diagrams this other methods computing -matrix, which are also developed.