Scattering amplitudes in non-Fermi-liquid systems

By a mix of form factors and analyticity techniques, we determine some fundamental scattering amplitudes in non-Fermi-liquid systems. These include the reflection and transmission amplitudes for Laughlin quasiparticles at a point contact between two g=1/2 Luttinger liquids, and the e-->e, lqp-->lqp and e-->e(edge) at a point contact between a Fermi liquid and a g=1/3 Luttinger liquid (all liquids chiral or not). These results are obtained in closed form, and give rise to rather simple expressions for the probabilities of the most basic processes of non-Fermi-liquid physics at these special values of the couplings.