On the effective interaction in the light-cone QCD-Hamiltonian

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. Emphasis is put on dealing with the many-body aspects of gauge field theory, and it is shown explicitly how the higher Fockspace amplitudes can be retrieved self-consistently from solutions in the qq̄-space. The approach is based on the novel method of iterated resolvents and on discretized lightcone 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. It is emphasized that vertex regularization as opposed to Fock-space regularization allows an explicit renormalization, which yields linear confinement. The string constant must be determined from experiment. Preprint MPIH-V26-1997 Submitted to Physical Review D PACS-Index: 11.10Ef, 11.15Tk, 12.38Lg, 12.40Yx