I have worked with Kurt Haller, and Lusheng Chen, on constructing
coherent states that implement Gauss's law in 3+1 dimensional QCD in the
temporal gauge. Because the gauge fields themselves carry the charge of QCD, it
is both much more difficult and important to satisfy Gauss's law in QCD than in
QED. Feynman emphasized the possible importance of the proper implementation of
Gauss's law in non-Abelian gauge theories in understanding confinement.
Preliminary results of our work for a 'pure glue' 3+1 dimensional non-Abelian
gauge theory in the temporal gauge have been reported at the International
Workshops on Light-Cone Quantization at Dallas, Telluride, and Gran Sasso and
appear in the proceedings of the Dallas and Gran Sasso meetings. The 'pure glue'
work is reported in in Physics Letters B Vol. 373, 185 (1996) and also appears
in hep-th/9510037.
We have continued this investigation by extending the pure glue states to those
that are annihilated by the entire Gauss's law operator. We have also
constructed gauge-invariant operator-valued gauge and quark fields. These
results were discussed in invited talks Lusheng Chen and I gave at the 6th
International Workshop on Light-Front Quantization and Non-Perturbative QCD in
June and 1997 and also appears as Phys. Rev. D 55, 2347 (1997) and as hep-ph/9609507.
The purpose of this work is to shift canonically quantized QCD closer to the
physical degrees of freedom. We are currently investigating the possible role in
QCD dynamics of the gauge-invariant operators and states in QCD that we have
constructed and appears in Phys. Lett. B403, 316 (1997), and as hep-th/9703139.