  We give a brief summary of the current status of the electron many-body
problem in graphene. We claim that graphene has intrinsic dielectric properties
which should dress the interactions among the quasiparticles, and may explain
why the observation of electron-electron renormalization effects has been so
elusive in the recent experiments. We argue that the strength of Coulomb
interactions in graphene may be characterized by an effective fine structure
constant given by
$\alpha^{\star}(\mathbf{k},\omega)\equiv2.2/\epsilon(\mathbf{k},\omega)$, where
$\epsilon(\mathbf{k},\omega)$ is the dynamical dielectric function. At long
wavelengths, $\alpha^{\star}(\mathbf{k},\omega)$ appears to have its smallest
value in the static regime, where $\alpha^{\star}(\mathbf{k}\to0,0)\approx1/7$
according to recent inelastic x-ray measurements, and the largest value in the
optical limit, where $\alpha^{\star}(0,\omega)\approx2.6$. We conclude that the
strength of Coulomb interactions in graphene is not universal, but depends
highly on the scale of the phenomenon of interest. We propose a prescription in
order to reconcile different experiments.
