2019 Impact factor 4.389
Particles and Fields
Eur. Phys. J. C 7, 289-303
DOI 10.1007/s100529800994

On confinement in a light-cone Hamiltonian for QCD

H.C. Pauli

Max-Planck-Institut für Kernphysik, Postfach 103980, D-69029 Heidelberg, Germany (e-mail: pauli@mpi-hd.mpg.de)

Received: 27 March 1998 / Revised version: 3 June 1998 / Published online: 16 September 1998

The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions and in the light-cone gauge 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 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. Approximations are done to the non-truncated formalism. Together with vertex as opposed to Fock-space regularization, the method allows to apply the renormalization programme non-perturbatively to a Hamiltonian. The conventional QCD scale is found arising from regulating the transversal momenta. It conspires with additional mass scales to produce possibly confinement.

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