Bosonic description of a Tomonaga-Luttinger model with impurities

We extend a recently proposed non-local version of Colemanʹs equivalence between the Thirring and sine-Gordon models to the case in which the original fermion fields interact with fixed impurities. We explain how our results can be used in the context of one-dimensional strongly correlated systems (the so called Tomonaga-Luttinger model) to study the dependence of the charge-density oscillations on the range of the fermionic interactions.