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Theoretical Particle Physics

Constrained States in non-Abelian Gauge Theories

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.