  We develop a nonperturbative zero-temperature theory for the dynamic response
functions of interacting one-dimensional spin-1/2 fermions. In contrast to the
conventional Luttinger liquid theory, we take into account the nonlinearity of
the fermion dispersion exactly. We calculate the power-law singularities of the
spectral function and the charge and spin density structure factors for
arbitrary momenta and interaction strengths. The exponents characterizing the
singularities are functions of momenta and differ significantly from the
predictions of the linear Luttinger liquid theory. We generalize the notion of
the spin-charge separation to the nonlinear spectrum. This generalization leads
to phenomenological relations between threshold exponents and the threshold
energy.
