Abstract
We describe a renormalization group method to study the localized-delocalized transition of a one-dimensional interacting electron gas in a random potential. We obtain the phase diagram and the exponents of the correlation functions in the delocalized regime. The boundary between the two regimes is found to depend both on disorder and on the strength of the interactions. The delocalized phase is dominated by superconducting fluctuations. We find the asymptotic behaviour of the localization length and the temperature dependence of the conductivity. An analogous description is developed for the localized-superfluid transition of a one-dimensional boson gas. In this case the transition to the localized regime occurs for increasingly repulsive interactions.