Abstract The S-matrix for each chiral sector of Liouville theory on a cylinder is computed from the loop expansion of correlation functions of a one-dimensional field theory on a circle with a non-local kinetic energy and an exponential potential. This action is the Legendre transform of the generating function of semiclassical scattering amplitudes. It is derived from the relation be... https://njjtzknsdxuw.dsiblogger.com/67921449/managing-food-quality-risk-in-global-supply-chain-a-risk-management-framework