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We study the dual Higgs mechanism induced by monopole condensation based on the dual gauge formalism in the maximally abelian (MA) gauge in the lattice QCD. To examine ``monopole condensation'' in QCD, we study the monopole part or the monopole-current system appearing in the MA gauge by extracting the dual gluon field $B_\mu$. First, we investigate the inter-monopole potential using the dual Wilson loop in the lattice QCD simulation. In the monopole part in the MA gauge, the inter-monopole potential is found to be flat, and can be fitted as the Yukawa potential in the infrared region. From more detailed analysis of the inter-monopole potential considering the monopole size, we estimate the effective dual-gluon mass $m_B \simeq 0.5$GeV and the effective monopole size $R_{^{_{\rm M}}} \simeq 0.2$fm. Second, we study the dual gluon propagator $G^D_{\mu\nu}(x-y) \equiv < B_\mu(x) B_\nu(y) >_{\rm MA}$ in the MA gauge, and find that $G^D_{\mu\mu}$ behaves as the massive vector-boson propagator with $m_B \simeq 0.4$ GeV in the infrared region. The effective-mass acquirement of the dual gluon field $B_\mu$ at the long distance can be regarded as the lattice QCD evidence of ``infrared monopole condensation'' in the MA gauge.

Using the SU(2) lattice QCD, we formulate the dual Wilson loop and study the dual Higgs mechanism induced by monopole condensation in the maximally abelian (MA) gauge, where QCD is reduced into an abelian gauge theory including the electric current $j_\mu$ and the monopole current $k_\mu$. After the abelian projection in the MA gauge, the system can be separated into the photon part and the monopole part corresponding to the separation of $j_\mu$ and $k_\mu$, respectively. We study here the monopole part (the monopole-current system), which is responsible to the electric confinement. Owing to the absence of electric currents, the monopole part is naturally described using the dual gluon field $B_\mu$ without the Dirac-string singularity. Defining the dual Wilson loop from the dual gluon $B_\mu$, we find the perimeter law of the dual Wilson loop in the lattice QCD simulation. In the monopole part in the MA gauge, the inter-monopole potential is found to be flat, and can be fitted as the Yukawa potential in the infrared region after the subtraction of the artificial finite-size effect on the dual Wilson loop. From more detailed analysis of the inter-monopole potential considering the monopole size, we estimate the effective dual-gluon mass $m_B \simeq 0.5$GeV and the effective monopole size $R \simeq 0.2$fm. The effective mass of the dual gluon field at the long distance can be regarded as an evidence of ``infrared monopole condensation''.

We study the confinement physics in QCD in the maximally abelian (MA) gauge using the SU(2) lattice QCD, based on the dual-superconductor picture. In the MA gauge, off-diagonal gluon components are forced to be small, and the off-diagonal angle variable $\chi_\mu(s)$ tends to be random. Within the random-variable approximation for $\chi_\mu(s)$, we analytically prove the perimeter law of the off-diagonal gluon contribution to the Wilson loop in the MA gauge, which leads to abelian dominance on the string tension. To clarify the origin of abelian dominance for the long-range physics, we study the charged-gluon propagator in the MA gauge using the lattice QCD, and find that the effective mass $m_{ch} \simeq 0.9 {\rm GeV}$ of the charged gluon is induced by the MA gauge fixing. In the MA gauge, there appears the macroscopic network of the monopole world-line covering the whole system, which would be identified as monopole condensation at a large scale. To prove monopole condensation in the field-theoretical manner, we derive the inter-monopole potential from the dual Wilson loop in the monopole part of QCD, which carries the nonperturbative QCD aspects, in the MA gauge. The dual gluon mass is evaluated as $m_B \simeq $0.5GeV in the monopole part in the infrared region, which is the evidence of the dual Higgs mechanism by monopole condensation., Comment: Talk given at Int. Workshop on ``Future Directions in Quark Nuclear Physics''(QNP98), Adelaide, Australia, Mar. 1998, and to be published in the Proceedings (World Scientific)

We study the dual Wilson loop and the inter-monopole potential(the static potential between the color magnetic monopoles) in the maximally abelian gauge to clarify the dual Higgs mechanism induced by monopole condensation. There is no (color-)electric current in the monopole part, which includes the essence of the nonperturbative QCD, and hence the system can be described by the dual gauge field $B_\mu$ without the singularity like the Dirac string. We find that the dual Wilson loop seems to obey the perimeter law, and the inter-monopole potential becomes Yukawa-type in the infrared region. From the inter-monopole potential, we estimate the dual gluon mass $m_B$ and the effective size $R$ of the monopole: $m_B \simeq 0.5$GeV, $R \simeq 0.35$fm., Comment: Talk presented by A. Tanaka at ``INNOCOM '97'', XVII RCNP the International Symposium on Innovative Computational Methods in Nuclear Many-Body Problems, 10 - 15 November 1997, in Osaka, Japan, 3 pages, Plain Latex

We study the correlation between instantons and QCD-monopoles both in the lattice gauge theory and in the multi-instanton system using the maximally abelian gauge. First, we find the existence of an almost linear correlation between the total length of monopole trajectories and the total number of pseudoparticles (instantons and anti-instantons) in the $16^{3}\times4$ SU(2) lattice. Second, we study the features of QCD-monopole in the SU(2) multi-instanton vacuum on the $16^{4}$ lattice as a random ensemble of pseudoparticles. A signal of monopole condensation is found as the clustering of monopole trajectories, when the topological pseudoparticles is sufficiently dense., Talk presented by S. Sasaki at International Conference on Quark Confinement and the Hadron Spectrum II, Como, Italy, 26-29 Jun 1996. Latex, uses epsf.tex and sprocl.sty, 4 pages, 3 postscript figures included