EXACT QUANTUM S-MATRIX IN THE LIOUVILLE FIELD-THEORY

Classical scattering in the Liouville held theory (LFT) is essentially finite-dimensional, and in some cases the classical S-matrix can be represented as a transformation of the Poisson group SL(2, I). Motivated by this and using conjectural quantum analogues of some ingredients of the classical model, we find an exact quantum S-matrix without constructing the quantum LFT in full. The quantum S-matrix is explicitly represented as a transformation of the quantum group SL(q)(2, I), and for a particular implementation, the S-matrix is shown to be unitary (unitarily generated).