On Deriving the E ective Interaction from the QCD - Lagrangian

The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions is mapped non-perturbatively on an e ective 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-Danco 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 eld theory. Important is that the higher Fock-space amplitudes can be retrieved self-consistently from these solutions.