In the previous chapter, we formalized the parton model in a simple quantum field theory. A number of further developments follow fairly simply, and this chapter's purpose is to give an account of them, before we go on to the full QCD treatment.

We first extend the parton model for DIS to the very important case of charged-current weak-interaction processes. Then we examine a particularly influential form of perturbation theory: light-front (or x+-ordered) perturbation theory. After that I present the light-front quantization of gauge theories, a natural extension of what we did earlier for non-gauge theories. We will thereby be able to introduce appropriate definitions for parton densities in a gauge theory, and to convert them to a gauge invariant form with the aid of what are known as Wilson-line operators.

DIS with weak interactions, neutrino scattering, etc.

We have extensively discussed DIS for the case of virtual photon exchange. The same principles apply equally to all lepto-production processes l + N → l′ + X, and thus they apply whether the exchanged electroweak boson is a W, Z or photon. There are a large number of different cases, and, as far as the theory by itself is concerned, all are a minor variation on the purely electromagnetic case, both at the parton-model level, and with all the QCD modifications.