The global S U(3) color symmetry and its physical consequences are discussed.The N(o)ther current is actually governed by the conserved matter current of color charges if the color field generated by this charge is properly polarized.The color field strength of a charge can have a uniform part due to the nontrivial QCD vacuum field and the nonzero gluon condensate,which implies that the self-energy of a system with a net color charge is infinite and,therefore,cannot exist as a free state.This is precisely what color confinement means.Accordingly,the Comell type potential with the feature of Casimir scaling is derived for a color singlet system composed of a static color charge and an anti-charge.The uniform color field also implies that a hadron has a minimal size and minimal energy.Furthermore,the global S U(3) color symmetry requires that the minimal irreducible color singlet systems can only be q(q),qqq,gg,ggg,q(q)g,qqqg,(q)(q)(q)g,etc.,therefore a multi-quark system can only exist as a molecular configuration if there are no other binding mechanisms.