  The dynamical conductivity of interacting multiband electronic systems
derived in Ref.[1] is shown to be consistent with the general form of the Ward
identity. Using the semiphenomenological form of this conductivity formula, we
have demonstrated that the relaxation-time approximation can be used to
describe the damping effects in weakly interacting multiband systems only if
local charge conservation in the system and gauge invariance of the response
theory are properly treated. Such a gauge-invariant response theory is
illustrated on the common tight-binding model for conduction electrons in
hole-doped graphene. The model predicts two distinctly resolved maxima in the
energy-loss-function spectra. The first one corresponds to the intraband
plasmons (usually called the Dirac plasmons). On the other hand, the second
maximum ($\pi$ plasmon structure) is simply a consequence of the van Hove
singularity in the single-electron density of states. The dc resistivity and
the real part of the dynamical conductivity are found to be well described by
the relaxation-time approximation, but only in the parametric space in which
the damping is dominated by the direct scattering processes. The ballistic
transport and the damping of Dirac plasmons are thus the questions that require
abandoning the relaxation-time approximation.
