Exact current-current Green functions in strongly correlated 1D systems with impurity

We derive an exact expression for the Kubo conductunce in the Quantum Hall device with the point-like intra-edge backscattering. This involves the calculation of current-current correlator exactly, which we perform using form-factor method. In brief, the full set of intermediate states is inserted in the correlator, and for each term the closed mathematical expression is obtained. It is shown that by making a special choice of intermediate states in accordance with the hidden symmetries of the model, one achieves fast convergence of the series, thus proving the form-factor approach to be especially powerfull. This review is based on the joint work with H.Saleur and F.Lesage.