  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.
