Nonuniversal prefactors in the correlation functions of one-dimensional quantum liquids

We develop a general approach to calculating ``nonuniversal'' prefactors in static and dynamic correlation functions of one-dimensional (1D) quantum liquids at zero temperature by relating them to the finite-size scaling of certain matrix elements (form factors). This represents a powerful tool for extracting data valid in the thermodynamic limit from finite-size effects. As the main application, we consider weakly interacting spinless fermions with an arbitrary pair interaction potential, for which we perturbatively calculate certain prefactors in static and dynamic correlation functions. We also evaluate prefactors of the long-distance behavior of correlation functions nonperturbatively for the exactly solvable Lieb-Liniger model of 1D bosons.