Schwinger–Dyson approach to Liouville field theory

We discuss Liouville field theory in the framework of the Schwinger–Dyson approach and derive a functional equation for the three-point structure constant. We prove the existence of a second Schwinger–Dyson equation based on the duality between the screening charge operators and obtain a second functional equation for the structure constant. We use the system of these two equations to uniquely determine the structure constant.