  We study the unscreened Coulomb interaction in a one-dimensional electron
system at low-energy. We use renormalization group methods and a GW
approximation, in order to analyze the model. This yields both a strong
wavefunction renormalization and a renormalization of the Fermi velocity. The
significance of the effects depends on the filling level of the Fermi system.
Despite the long-range character of the interaction, the system still falls
into the Luttinger liquid universality class, since the effective couplings
remain bounded at arbitrarily low energies.
