UMKLAPP PROCESSES FOR ELECTRONS AND THEIR RENORMALIZATION-GROUP FLOW

We study umklapp couplings and their renormalization-group flow for el ectrons in a two-dimensional lattice. It is shown that the effective l ow-energy Hamiltonian involves not only forward scattering, but also c onsiderable nonforward umklapp scattering, when the electrons fill a s ubstantial fraction of the valence band. The behavior of these couplin gs under the renormalization group is studied in the loop expansion. I t is shown that they remain marginal. We conclude with the possible co nsequences of this on properties of such electronic systems and their Fermi-liquid theory.