  We compute structure functions in the Hamiltonian formalism on a momentum
lattice using a physically motivated regularisation that links the maximal
parton number to the lattice size. We show for the $\phi ^4 _{3+1}$ theory that
our method allows to describe continuum physics. The critical line and the
renormalised mass spectrum close to the critical line are computed and scaling
behaviour is observed in good agreement with L{\"u}scher and Weisz' lattice
results. We then compute distribution functions and find a $Q^2$ behaviour and
the typical peak at $x_B\rightarrow 0$ like in $QCD$.
