Form factors approach to current correlations in one-dimensional systems with impurities

We show how to compute analytically time and space dependent correlations in one-dimensional quantum integrable systems with an impurity. Our approach is based on a description of these systems in terms of massless scattering of quasi-particles, Correlators follow then from matrix elements of local operators between multiparticle states, the ''massless form factors''. Although an infinite sum of these form factors has to be considered in principle, we find that for current, spin, and energy operators, only a few (typically two or three) are necessary to obtain an accuracy of more than 1%, for arbitrary coupling strength, that is all the way from short to large distances, As examples we compute, at zero temperature, the frequency-dependent conductance in a Luttinger liquid with impurity, the spectral function in the double-well problem of dissipative quantum mechanics and part of the space-dependent susceptibility in the Kondo model.