Nonperturbative Weak-Coupling Analysis of the Liouville Quantum Field Theory

A systematic weak-coupling expansion is developed for the Liouville quantum field theory on a periodic spatial interval. Matrix elements of various Liouville operators are computed to order $g^8$ by perturbation in nonzero modes about the exact solution of the zero-mode problem. To this order the results agree with the explicit operator solution given previously by Braaten, Curtright, and Thorn, in which the Liouville field was expressed in terms of a free pseudoscalar field by means of an operator Bäcklund transformation.