Color-singlet condensation in quantum chromodynamics and flux squeezing

Abstract

The nonperturbative condensation of the operator ${G_{\mu \nu }}^2$ in quantum chromodynamics is discussed using the renormalization-group technique. It is shown that magnetic condensation, $〈{G_{\mu \nu }}^2〉>0\mathrm{}$, leads to a new vacuum which has lower energy than the perturbative vacuum. From this fact it is concluded that Green's functions calculated in the normal vacuum have tachyonic singularities. By assuming the gauge-invariant local expansion of the effective action it is shown that the condensed vacuum has the property of a vanishing dielectric constant. If the color electric field is applied by introducing heavy quarks at infinity, the condensation is partly broken and there is a consistent solution in which an infinite tube of the color electric flux is formed. Arguments used rely heavily on the instability of the normal vacuum and on the negative character of the $\beta$ function. An attempt at the mean-field-type approximation is made. Comparison with the previous phenomenological approach is also given.