  Using a non-perturbative functional renormalization group approach involving
both fermionic and bosonic fields we calculate the interaction-induced change
of the Fermi surface of spinless fermions moving on two chains connected by
weak interchain hopping t_{bot}. We show that interchain backscattering can
strongly reduce the distance Delta between the Fermi momenta associated with
the bonding and the antibonding band, corresponding to a large reduction of the
effective interchain hopping t_{bot}^{*} A self-consistent one-loop
approximation neglecting marginal vertex corrections and wave-function
renormalizations predicts a confinement transition for sufficiently large
interchain backscattering, where the renormalized t_{bot}^{*} vanishes.
However, a more accurate calculation taking vertex corrections and
wave-function renormalizations into account predicts only weak confinement in
the sense that 0< | t_{bot}^{*} | << | t_{bot} |. Our method can be applied to
other strong-coupling problems where the dominant scattering channel is known.
