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We suggest a Hamiltonian formulation on a momentum lattice using a physicallymotivated regularization using the Breit-frame which links the maximal partonnumber to the lattice size. This scheme restricts parton momenta to positivevalues in each spatial direction. This leads to a drastic reduction of degreesof freedom compared to a regularization in the rest frame (center at zeromomentum). We discuss the computation of physical observables like (i) massspectrum in the critical region, (ii) structure and distribution functions,(iii) $S$-matrix, (iv) finite temperature and finite density thermodynamics inthe Breit-frame regularization. For the scalar $\phi^{4}_{3+1}$ theory wepresent numerical results for the mass spectrum in the critical region. Weobserve scaling behavior for the mass of the ground state and for some higherlying states. We compare our results with renormalization group results byL\"uscher and Weisz. Using the Breit-frame, we calculate for $QCD$ the relationbetween the $W^{\mu \nu}$ tensor, structure functions (polarized andunpolarized) and quark distribution functions. We use the improved parton-modelwith a scale dependence and take into account a non-zero parton mass. In theBjorken limes we find the standard relations between $F_{1}$, $F_{2}$, $g_{1}$and the quark distribution functions. We discuss the r\^ole of helicity. Wepresent numerical results for parton distribution functions in the scalarmodel. For the $\phi^{4}$-model we find no bound state with internal partonstructure. For the $\phi^{3}$-model we find a distribution function with partonstructure similar to Altarelli-Parisi behavior of $QCD$.Comment: 20 pages, four figure

Physics from Breit-frame regularization of a lattice Hamiltonian