Instantons and Monopoles in the Nonperturbative QCD

We study the confinement physics in QCD in the maximally abelian (MA) gaugeusing the SU(2) lattice QCD. To clarify the origin of abelian dominance for thelong-range physics, we study the charged-gluon propagator in the lattice QCD,and find that the effective mass $m_{ch} \simeq 0.9 {\rm GeV}$ of the chargedgluon is induced by the MA gauge fixing. In the MA gauge, there appears theglobal network of the monopole world-line covering the whole system, whichwould be identified as monopole condensation at a large scale. To provemonopole condensation, we apply the dual gauge formalism to the monopole part,and derive the inter-monopole potential from the dual Wilson loop in the MAgauge. In the monopole part, which carries the nonperturbative aspects of QCD,the dual gluon mass is evaluated as $m_B \simeq $0.5GeV, which is the evidenceof the dual Higgs mechanism by monopole condensation. As for the monopolestructure, the large fluctuation of off-diagonal gluons remains around themonopole in the MA gauge, and large cancellation occurs between the diagonaland off-diagonal action densities to keep the total QCD action finite. Thecharged-gluon rich region around the QCD-monopole would provide the effectivemonopole size as the critical scale of the abelian projected QCD. Instantonsare expected to appear in the charged-gluon rich region around the monopoleworld-line in the MA gauge, which leads to the local correlation betweenmonopoles and instantons.Comment: Invited Lecture presented by H. Suganuma at 1997 Yukawa International Seminar (YKIS'97) on `` Non-Perturbative QCD -Structure of the QCD Vacuum-'', 2-12 December 1997, in Kyoto, Japan, 12 pages, Plain Late