On confinement in a light-cone Hamiltonian for QCD |
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Authors: | HC Pauli |
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Institution: | (1) Max-Planck-Institut für Kernphysik, Postfach 10 39 80, D-69029 Heidelberg, Germany (e-mail: pauli@mpi-hd.mpg.de) , DE |
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Abstract: | 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 -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.
Received: 27 March 1998 / Revised version: 3 June 1998 / Published online: 16 September 1998 |
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