  We compute the spectral function rho(q,omega) of the one- dimensional
Luttinger model. We discuss the distinct influences of charge-spin separation
and of the anomalous dimensions of the fermion operators and their evolution
with correlation strength. Charge-spin separation shows up in finite spectral
weight at frequencies between v_sigma * q and v_rho * q where v_rho and v_sigma
are the velocities of charge and spin fluctuations while spectral weight above
v_rho * q and below -v_rho * q is generated by the hybridization of the Fermi
surface at +/-k_F by interactions. There are nonuniversal power-law
singularities at these special frequencies. We discuss the consistency of
recent photoemission experiments on low-dimensional conductors with a Luttinger
liquid picture which then would suggest very strong long- range interactions.
It is pointed out that many-particle correlation functions in principle exhibit
similar singularities but they probe different and complementary aspects of the
Fermi surface interactions.
