UMKLAPP SCATTERING IN FERMI LIQUIDS - A RENORMALIZATION-GROUP APPROACH

The role of Umklapp scattering for electrons on a lattice is studied. Using renormalisation group methods it is shown that the effective low energy interaction involves not only forward scattering, but also non -forward Umklapp scattering. We show that the latter can happen to alm ost all of the electrons even when they have a filling of around one-h alf. The behavior of these Umklapp couplings is studied in the loop ex pansion. It is shown that they remain marginal to all loop orders. The discussion is given in the context of two-dimensional lattices, but g eneralisation to three-dimensions is mentioned. We also briefly discus s the possible consequences of this on Fermi liquid theory and on phys ical properties of such electronic systems.