| We develop a general approach to calculating "non-universal" prefactors in static and dynamic correlation functions of 1D quantum liquids, by relating them to the finite 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 applications, 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. |
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