  Using functional renormalization group methods, we present a self-consistent
calculation of the true Fermi momenta k_F^a (antibonding band) and k_F^b
(bonding band) of two spinless interacting metallic chains coupled by small
interchain hopping. In the regime where the system is a Luttinger liquid, we
find that Delta = k_F^b - k_F^a is self-consistently determined by Delta =
Delta_{1} [ 1 + {g}_0^2 ln (Lambda_0 / Delta)^2]^{-1} where g_0 is the
dimensionless interchain backscattering interaction, Delta_{1} is the
Hartree-Fock result for k_F^{b}-k_F^a, and Lambda_0 is an ultraviolet cutoff.
If {g}_0^2 ln (Lambda_0 / Delta_{1})^2 is much larger than unity than even weak
interachain backscattering leads to a strong reduction of the distance between
the Fermi momenta.
