Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1997-07-16
Physics
High Energy Physics
High Energy Physics - Phenomenology
23 pages, 6 figures, Latex; to be submitted to PhysRevD. PACS-Index: 11.10Ef, 11.15Tk, 12.38Lg, 12.40Yx
Scientific paper
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.
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