  We demonstrate that the plasmon frequency and Drude weight of the electron
liquid in a doped graphene sheet are strongly renormalized by electron-electron
interactions even in the long-wavelength limit. This effect is not captured by
the Random Phase Approximation (RPA), commonly used to describe electron fluids
and is due to coupling between the center of mass motion and the pseudospin
degree of freedom of the graphene's massless Dirac fermions. Making use of
diagrammatic perturbation theory to first order in the electron-electron
interaction, we show that this coupling enhances both the plasmon frequency and
the Drude weight relative to the RPA value. We also show that interactions are
responsible for a significant enhancement of the optical conductivity at
frequencies just above the absorption threshold. Our predictions can be checked
by far-infrared spectroscopy or inelastic light scattering.
