Classical and quantal Liouville field theory

The canonical structure of the Liouville theory is investigated. We present two canonical transformations which map the theory onto a free field theory. The first makes use of conformal invariance and relies on a Yang-Feldman solution to the field equation. The second employs the inverse scattering method, which is uncommonly intricate, owing to the conformal invariance. We also analyze the quantized theory. Semiclassical arguments, supplemented by a study of the exact effective potential, suggest that the theory has a conformally invariant, continuous energy spectrum, bounded from below, but no translationally invariant ground state.