  A continuous unitary transformation is introduced which realizes Landau's
mapping of the elementary excitations (quasi-particles) of an interacting Fermi
liquid system to those of the system without interaction. The conservation of
the number of quasi-particles is important. The transformation is performed
numerically for a one-dimensional system, i.e. the worst case for a Fermi
liquid approach. Yet evidence for Luttinger liquid behavior is found. Such an
approach may open a route to a unified description of Fermi and Luttinger
liquids on all energy scales.
