We construct the quantum mechanical field operator of the two-dimensional Liouville theory in a finite box. This leads us to the discovery of a new type of triangle relation which does not reduce to the already known ones. We apply our result to the construction of the string model in an arbitrary number of space-time dimensions D . We show that there are no tachyons in −∞< D⩽1 , and we indicate how to continue to D >1, which is a strong-coupling region for the Liouville field theory.