ar X iv : 0 80 8 . 26 65 v 2 [ he p - ph ] 4 S ep 2 00 8 Rapidity divergences and valid definitions of parton densities

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.