  We address the computation of physical observables in graphene in the
presence of Coulomb interactions of density-density type modeled with a static
Coulomb potential within a quantum field theory perturbative renormalization
scheme. We show that all the divergences encountered in the physical quantities
are associated to the one loop electron self-energy and can be determined
without ambiguities by a proper renormalization of the Fermi velocity. The
renormalization of the photon polarization to second order in perturbation
theory - a quantity directly related to the optical conductivity - is given as
an example.
