  We consider serious conceptual problems with the application of standard
perturbation theory, in its zero temperature version, to the computation of the
dressed Fermi surface for an interacting electronic system. In order to
overcome these difficulties, we set up a variational approach which is shown to
be equivalent to the renormalized perturbation theory where the dressed Fermi
surface is fixed by recursively computed counterterms. The physical picture
that emerges is that couplings that are irrelevant tend to deform the Fermi
surface in order to become more relevant (irrelevant couplings being those that
do not exist at vanishing excitation energy because of kinematical constraints
attached to the Fermi surface). These insights are incorporated in a
renormalization group approach, which allows for a simple approximate
computation of Fermi surface deformation in quasi one-dimensional electronic
conductors. We also analyze flow equations for the effective couplings and
quasiparticle weights. For systems away from half-filling, the flows show three
regimes corresponding to a Luttinger liquid at high energies, a Fermi liquid,
and a low-energy incommensurate spin-density wave. At half-filling Umklapp
processes allow for a Mott insulator regime where the dressed Fermi surface is
flat, implying a confined phase with vanishing effective transverse
single-particle coherence. The boundary between the confined and Fermi liquid
phases is found to occur for a bare transverse hopping amplitude of the order
of the Mott charge gap of a single chain.
