  The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in
3+1 dimensions and in the light-cone gauge is mapped non-perturbatively on an
effective Hamiltonian which acts only in the Fock space of a quark and an
antiquark. Emphasis is put on the many-body aspects of gauge field theory, and
it is shown explicitly how the higher Fock-space amplitudes can be retrieved
self-consistently from solutions in the $q\bar q$-space. The approach is based
on the novel method of iterated resolvents and on discretized light-cone
quantization driven to the continuum limit. It is free of the usual
perturbative Tamm-Dancoff truncations in particle number and coupling constant
and respects all symmetries of the Lagrangian including covariance and gauge
invariance. Approximations are done to the non-truncated formalism. Together
with vertex as opposed to Fock-space regularization, the method allows to apply
the renormalization programme non-perturbatively to a Hamiltonian. The
conventional QCD scale is found arising from regulating the transversal
momenta. It conspires with additional mass scales to produce possibly
confinement.
