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

Abstract

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 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. 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.