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On the basis of the Fermi liquid theory, we investigate the many-body effecton the Drude weight. In a lattice system, the Drude weight $D$ is modified byelectron-electron interaction due to Umklapp processes, while it is notrenormalized in a Galilean invariant system. This is explained by showing thatthe effective mass $m'$ for $D\propto n/m'$ is defined through the current, notvelocity, of quasiparticle. It is shown that the inequality $D>0$ is requiredfor the stability against the uniform shift of the Fermi surface. The result ofperturbation theory applied for the Hubbard model indicates that $D$ as afunction of the density $n$ is qualitatively modified around half filling$n\sim 1$ by Umklapp processes.Comment: 20 pages, 2 figures; J. Phys. Soc. Jpn. Vol.67, No.

Electrical Conductivity of Fermi Liquids. I. Many-Body Effect on the Drude Weight