Towards solving gauge-field theory

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. The effective interaction turns out to be the kernel of an integral equation in the momentum space of a single quark, which is frame-independent and solvable on comparatively small computers. Important is that the higher Fock-space amplitudes can be retrieved self-consistently from these solutions.