Form-factors computation of Friedel oscillations in Luttinger liquids

We show how the form-factors approach can be used to compute correlators of operators with non-trivial anomalous dimension in quantum impurity problems. This is done by a series of regularizations that cure completely the infrared, divergencies, without spoiling the exactedness of the method. As an application, we compute for g less than or equal to 1/2 the 'Friedel oscillations' of charge density induced by a single impurity in a one-dimensional Luttinger liquid of spinless electrons.