Quark Confinement and Color Transparency in a Gauge-Invariant Formulation of QCD

Abstract

We examine a nonlocal interaction that results from expressing the QCD Hamiltonian entirely in terms of gauge-invariant quark and gluon fields. The interaction couples one quark color-charge density to another, much as electric charge densities are coupled to each other by the Coulomb interaction in QED. In QCD, this nonlocal interaction also couples quark color-charge densities to gluonic color. We show how the leading part of the interaction between quark color-charge densities vanishes when the participating quarks are in a color singlet configuration, and that, for singlet configurations, the residual interaction weakens as the size of a packet of quarks shrinks. Because of this effect, color-singlet packets of quarks should experience final state interactions that increase in strength as these packets expand in size. For the case of an SU(2) model of QCD based on the ansatz that the gauge-invariant gauge field is a hedgehog configuration, we show how the infinite series that represents the nonlocal interaction between quark color-charge densities can be evaluated nonperturbatively, without expanding it termby-term. We discuss the implications of this model for QCD with SU(3) color and a gauge-invariant gauge field determined by QCD dynamics. *

Charges from Dressed Matter: Construction

“…Essentially there is a minimal perturbative extension of the QED result which retains gauge invariance. We note that Haller and his collaborators [37,38] have also obtained perturbative formulae which agree with this minimal extension of the static charge (5).…”

“…The connection between this, by construction the positive frequency part of B, and the gauge and matter fields will be clarified in Eq (37)…”

Untitled

“…It is a pleasure to dedicate this work to Prof. Kurt Haller, who has been recently interested in color transparency [15], and who has long been interested in the fundamentals of QCD as applied to light-cone physics [16]. Happy birthday, Kurt, and our best wishes for many more to come.…”

What can we learn about Gribov copies from a formulation of QCD in terms of gauge-invariant fields?

“…We have been able to express the QCD Hamiltonian entirely in terms of gauge-invariant field operators 14,15,16 . For that purpose, we have defined gauge-invariant versions of Π a i and of the Gauss's law operator.…”