Exact quantum S-matrix in the Liouville field theory

Abstract

Classical scattering in the Liouville field 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,R). 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 SLq(2, R), and for a particular implementation, the S-matrix is shown to be unitary (unitarily generated).