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 1D quantum liquids at zero temperature,
by relating them to the unite size scaling of certain matrix elements
(form factors). This represents a new, 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 non-perturbatively evaluate
prefactors of the long-distance behavior of correlation functions for the
exactly solvable Lieb-Liniger model of 1D bosons.