Gauge-Invariant QCD - an Approach to Long-Range Color-Confining Forces

Abstract

We discuss the transformation of the QCD temporal-gauge Hamiltonian to a representation in which it can be expressed as a functional of gauge-invariant quark and gluon fields. We show how this objective can be realized by implementing the non-Abelian Gauss's law, and by using the mathematical apparatus developed for that purpose to also construct gauge-invariant quark and gluon fields. We demonstrate that, in the transformed QCD Hamiltonian, the interactions of pure-gauge components of the gauge field with color-current densities are replaced by nonlocal interactions connecting quark color-charge densities to each other and to `glue'-color. We discuss the nonperturbative evaluation of these nonlocal interactions, which are non-Abelian analogs of the Coulomb interaction in QED, and we explore their implications for QCD in the low-energy regime.