Non-abelian Stokes Theorem and Quark Confinement in Qcd

To understand the Abelian dominance and magnetic monopole dominance in lowenergy QCD, we rewrite the non-Abelian Wilson loop into the form which is written in terms of its Abelian components or the ’t Hooft-Polyakov tensor describing the magnetic monopole. This is peformed by making use of a version of non-Abelian Stokes theorem. We propose a modified version of the maximal Abelian (MA) gauge. By adopting the modified MA gauge in QCD, we show that the off-diagonal gluons and Faddeev-Popov ghosts acquire their masses through the ghost–antighost condensation due to four ghost interaction coming from the gauge-fixing term of the modified MA gauge. The asymptotic freedom of the original nonAbelian gauge theory is preserved in this derivation.