  We suggest a Hamiltonian formulation on a momentum lattice using a physically
motivated regularization using the Breit-frame which links the maximal parton
number to the lattice size. This scheme restricts parton momenta to positive
values in each spatial direction. This leads to a drastic reduction of degrees
of freedom compared to a regularization in the rest frame (center at zero
momentum). We discuss the computation of physical observables like (i) mass
spectrum in the critical region, (ii) structure and distribution functions,
(iii) $S$-matrix, (iv) finite temperature and finite density thermodynamics in
the Breit-frame regularization. For the scalar $\phi^{4}_{3+1}$ theory we
present numerical results for the mass spectrum in the critical region. We
observe scaling behavior for the mass of the ground state and for some higher
lying states. We compare our results with renormalization group results by
L\"uscher and Weisz. Using the Breit-frame, we calculate for $QCD$ the relation
between the $W^{\mu \nu}$ tensor, structure functions (polarized and
unpolarized) and quark distribution functions. We use the improved parton-model
with a scale dependence and take into account a non-zero parton mass. In the
Bjorken 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. We
present numerical results for parton distribution functions in the scalar
model. For the $\phi^{4}$-model we find no bound state with internal parton
structure. For the $\phi^{3}$-model we find a distribution function with parton
structure similar to Altarelli-Parisi behavior of $QCD$.
