  We study quark confinement physics using lattice QCD. In the maximally
abelian (MA) gauge, the off-diagonal gluon amplitude is strongly suppressed,
and then the off-diagonal gluon phase shows strong randomness, which leads to a
large effective off-diagonal gluon mass, M_off=1.2GeV. Due to the large
off-diagonal gluon mass in the MA gauge, low-energy QCD is abelianized like
nonabelian Higgs theories. In the MA gauge, there appears a macroscopic network
of the monopole world-line covering the whole system. We extract and analyze
the dual gluon field B_mu from the monopole-current system in the MA gauge, and
evaluate the dual gluon mass as m_B = 0.4-0.5GeV in the infrared region, which
is a lattice-QCD evidence of the dual Higgs mechanism by monopole condensation.
Even without explicit use of gauge fixing, we can define the maximal abelian
projection by introducing a ``gluonic Higgs field'' phi(x), whose hedgehog
singularities lead to monopoles. From infrared abelian dominance and infrared
monopole condensation, infrared QCD is describable with the dual
Ginzburg-Landau theory. In relation to the color-flux-tube picture for baryons,
we study the three-quark (3Q) ground-state potential V_3Q in SU(3) lattice QCD
at the quenched level, with the smearing technique for enhancement of the
ground-state component. With accuracy better than a few %, V_3Q is well
described by a sum of the two-body Coulomb part and the three-body linear
confinement part sigma_3Q L_min, where L_min denotes the minimal value of the
total length of the color flux tube linking the three quarks. Comparing with
the Q-barQ potential, we find a universal feature of the string tension and the
OGE result for the Coulomb coefficient.
