Exactly Soluble Model for Umklapp Scattering at Quantum-Hall Edges

We consider the low-energy, long-wave-length excitations of a reconstructed quantum-Hall edge where three branches of chiral one-dimensional edge excitations exist. We find that, in addition to forward scattering between the three edge-excitation branches, Coulomb interaction gives rise to a novel Umklapp-type scattering process that cannot be accounted for within a generalized Tomonaga-Luttinger model. We solve the theory including Umklapp processes exactly in the long-wave-length limit and calculate electronic correlation functions.