  The theoretical description of interacting fermions in one spatial dimension
is simplified by the fact that the low energy excitations can be described in
terms of bosonic degrees of freedom. This fermion-boson transmutation (FBT)
which lies at the heart of the Luttinger liquid concept is presented in a way
which does not require a knowledge of quantum field theoretical methods. As the
basic facts can already be introduced for noninteracting fermions they are
mainly discussed. As an application we use the FBT to present exact results for
the low temperature thermodynamics and the occupation numbers in the
microcanonical and the canonical ensemble. They are compared with the standard
grand canonical results.
