Renormalization of Coulomb interaction in graphene: Determining observable quantities

We address the determination 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 discuss the similarities and differences of the model with quantum electrodynamics and show that all the divergences encountered in the physical quantities are associated to the electron self-energy and can be determined without ambiguities by a proper renormalization of the Fermi velocity and the electron wave function. 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. We also discuss the determination of the effective many-body coupling constant in graphene.