Restoration of the Local Gauge Symmetry and Color Confinement in Non-Abelian Gauge Theories

Restoration of the local gauge symmetry and its connection to color confinement is investigated in non-Abelian gauge theories with covariant gauge fixing. We consider the Noether current Jff,v of the local gauge transformation with transformation functions Ab(x) linear in Xp; Ab(x) =aabxv. This current is conserved only in the physical subspace of the state vector space and in perturbation theory contains a massless pole communicating to the gauge field. We define the local gauge symmetry restoration as the disappearance of this massless "Goldstone" pole from Jff,v. The restoration condition is obtained and it coincides exactly with the color confinement criterion proposed earlier by Kugo and Ojima. Quarks and other colored particles are shown to be confined in the local gauge symmetry restored phase by using the Ward identities of Jff.v.