Fermi liquids and fractional statistics in one dimension

Interacting fermion systems in one dimension, which in the low energy approximation are described by Luttinger liquid theory, can be reformulated as systems of weakly interacting particles with fractional exchange statistics. This is shown by use of Landau’s Fermi liquid theory, with quasiparticles interpreted as adiabatically dressed fermions. An application of this method is included, where boundary excitations of a two-dimensional quantum Hall electron system are studied.