Properties of a classical confining medium in SU2gluon dynamics

Abstract

We examine the properties of a classical non-Abelian system which can be interpreted as the ground state of an extended polarizable medium in Euclidean space. The medium is characterized by the value of two scalar order parameters, ${{G}_{\ensuremath{\mu}\ensuremath{\nu}}^{a}}^{*}{G}_{\ensuremath{\mu}\ensuremath{\nu}}^{a}=0$ and $\frac{1}{4}{G}_{\ensuremath{\mu}\ensuremath{\nu}}^{a}{G}_{\ensuremath{\mu}\ensuremath{\nu}}^{a}=\frac{3{\ensuremath{\sigma}}^{2}}{{g}^{2}}$. Starting from the assumption of time independence and spherical symmetry, we are able to find solutions to the classical field equations obeying these constraints and give simple analytic expressions for the vector potential, field-strength tensor, and polarization current in various gauges. We discuss gauge invariants formed from the fields and show that the classical analogs of Wilson loops display an area-law behavior.