  The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in
3+1 dimensions is mapped non-perturbatively on an effective Hamiltonian which
acts only in the Fock space of a quark and an antiquark. 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
Tamm-Dancoff truncations of the Fock space, rather the perturbative series are
consistently resumed to all orders in the coupling constant. Emphasis is put on
dealing with the many-body aspects of gauge field theory. Important is that the
higher Fock-space amplitudes can be retrieved self-consistently from these
solutions. (Proceedings Les Houches 1997)
