  Based on the dual superconductor picture, we study the confinement phenomena
systematically, using the lattice QCD, the monopole-current dynamics and the
dual Ginzburg-Landau (DGL) theory. (1) We study the origin of abelian dominance
for the confinement force in the maximally abelian (MA) gauge in terms of the
gluon-field properties using the lattice QCD. In the MA gauge, the off-diagonal
gluon amplitude is strongly suppressed, and the off-diagonal gluon phase tends
to be random, according to the weakness of the constraint from the QCD action.
Within the random-variable approximation for the off-diagonal gluon phase, we
show the perimeter law of the off-diagonal gluon contribution to the Wilson
loop, i.e. abelian dominance for the string tension, in the semi-analytical
manner. (2) We study the QCD-monopole structure in terms of the gluon field,
using the lattice QCD in the MA gauge. Around the monopole, both abelian and
off-diagonal parts of the QCD action become large, however, due to the
cancellation between them, monopoles can appear in QCD without large cost of
the QCD action. (3) We derive a simple relation between the confinement force
and the monopole density by idealizing the monopole contribution to the Wilson
loop. (4) We study the monopole current dynamics. (5) We consider the
derivation of the DGL theory from the monopole ensemble. (6) We study the QCD
phase transition at finite temperatures in the DGL theory. (7) We apply the DGL
theory for the hadron-bubble formation in early Universe and quark-gluon-plasma
formation process in the ultra-relativistic heavy-ion collision.

High Energy Physics - Lattice