  On the basis of the Fermi liquid theory, we investigate the many-body effect
on the Drude weight. In a lattice system, the Drude weight $D$ is modified by
electron-electron interaction due to Umklapp processes, while it is not
renormalized in a Galilean invariant system. This is explained by showing that
the effective mass $m'$ for $D\propto n/m'$ is defined through the current, not
velocity, of quasiparticle. It is shown that the inequality $D>0$ is required
for the stability against the uniform shift of the Fermi surface. The result of
perturbation theory applied for the Hubbard model indicates that $D$ as a
function of the density $n$ is qualitatively modified around half filling
$n\sim 1$ by Umklapp processes.
