Parton model and the Bethe-Salpeter wave function

The quark-parton model is discussed from the point of view that the quark partons are the quanta created by the Fourier transforms of the quark fields at constant $x^{+}$. We argue using this picture that, for a given behavior of a hadron's deep-inelastic structure function $W_2\mathrm{}\left(x\right)\mathrm{}$ as $x\to 1$, the Drell-Yan-West relation provides a lower bound on the behavior of its form factor $F_1\left(Q^2\right)$ as $Q^2\to \infty$. The connection between the parton and Bethe-Salpeter descriptions of hadron structure is described and used to translate known information about the pion's Bethe-Salpeter wave function into information about the amplitude for a pion to consist of precisely two quark partons. We find that the two-parton contributions to $\nu W_2\mathrm{}\left(x\right)\mathrm{}$ and $F\left(Q^2\right)$ behave roughly like $\nu W_2\propto {\mathrm{}(1-x)\mathrm{}}^2$ for small ($1-x$) and $F\left(Q^2\right)\propto {\left(Q^2\right)}^{-1\mathrm{}}$ for large $Q^2$, respectively.