  We suggest to compute structure functions in the Hamiltonian formalism on a
momentum lattice using a physically motivated regularisation that links the
total parton number to the lattice size. We show for the $\phi ^4 _4$ theory
that our method allows to describe continuum physics. The critical line and the
renormalised mass spectrum close to that critical line are computed and scaling
behaviour is observed in good agreement with the semi-analytical results of
L{\"u}scher and Weisz and with other lattice simulations. We also demonstrate
that our method is able to reproduce the $Q^2$ behaviour of deep inelastic
structure functions and the typical peak at $x_B=0.$
