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
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.
Copyright Springer-Verlag
