  I construct the spectral function of the Luther-Emery model which describes
one-dimensional fermions with one gapless and one gapped degree of freedom,
i.e. superconductors and Peierls and Mott insulators, by using symmetries,
relations to other models, and known limits. Depending on the relative
magnitudes of the charge and spin velocities, and on whether a charge or a spin
gap is present, I find spectral functions differing in the number of
singularities and presence or absence of anomalous dimensions of fermion
operators. I find, for a Peierls system, one singularity with anomalous
dimension and one finite maximum; for a superconductor two singularities with
anomalous dimensions; and for a Mott insulator one or two singularities without
anomalous dimension. In addition, there are strong shadow bands. I generalize
the construction to arbitrary dynamical multi-particle correlation functions.
The main aspects of this work are in agreement with numerical and Bethe Ansatz
calculations by others. I also discuss the application to photoemission
experiments on 1D Mott insulators and on the normal state of 1D Peierls
systems, and propose the Luther-Emery model as the generic description of 1D
charge density wave systems with important electronic correlations.
