  Rapidity divergences occur when parton densities in a gauge theory are
defined in the most natural way, as expectation values of partonic number
operators in light-front quantization. I review these and other related
divergences, and show how the definitions of parton densities can be modified
to remove the divergences. A modified definition is not only essential for many
phenomenological applications of QCD, but also concerns the treatment of parton
densities in non-perturbative approaches. The necessity of modifications in the
definition of a parton density also entails corrections in the formulation of
light-front quantization for gauge theories.
