  Motivated by recent optical measurements on a number of strongly correlated
electron systems, we revisit the dependence of the conductivity of a Fermi
liquid, \sigma(\Omega,T), on the frequency \Omega and temperature T. Using the
Kubo formalism and taking full account of vertex corrections, we show that the
Fermi liquid form Re\sigma^{-1}(\Omega,T)\propto \Omega^2+4\pi^2T^2 holds under
very general conditions, namely in any dimensionality above one, for a Fermi
surface of an arbitrary shape (but away from nesting and van Hove
singularities), and to any order in the electron-electron interaction. We also
show that the scaling form of Re\sigma^{-1}(\Omega,T) is determined by the
analytic properties of the conductivity along the Matsubara axis. If a system
contains not only itinerant electrons but also localized degrees of freedom
which scatter electrons elastically, e.g., magnetic moments or resonant levels,
the scaling form changes to Re\sigma^{-1}(\Omega,T)\propto \Omega^2+b\pi^2T^2,
with 1\leq b<\infty. For purely elastic scattering, b =1. Our analysis implies
that the value of b\approx 1, reported for URu_2Si_2 and some rare-earth based
doped Mott insulators, indicates that the optical conductivity in these
materials is controlled by an elastic scattering mechanism, whereas the values
of b\approx 2.3 and b\approx 5.6, reported for underdoped cuprates and
organics, correspondingly, imply that both elastic and inelastic mechanisms
contribute to the optical conductivity.
