  The general structure of semi-inclusive polarized electron scattering from
polarized spin-1/2 targets is developed for use at all energy scales, from
modest-energy nuclear physics applications to use in very high energy particle
physics. The leptonic and hadronic tensors that enter in the formalism are
constructed in a general covariant way in terms of kinematic factors that are
frame dependent but model independent and invariant response functions which
contain all of the model-dependent dynamics. In the process of developing the
general problem the relationships to the conventional responses expressed in
terms of the helicity components of the exchanged virtual photon are presented.
For semi-inclusive electron scattering with polarized electrons and polarized
spin-1/2 targets one finds that 18 invariant response functions are required,
each depending on four Lorentz scalar invariants. Additionally it is shown how
the semi-inclusive cross sections are related via integrations over the
momentum of the selected coincidence particle and sums over open channels.
