  We propose a novel description for the Higgs mechanism by which a gauge boson
acquires the mass. We do not assume spontaneous breakdown of gauge symmetry
signaled by a non-vanishing vacuum expectation value of the scalar field. In
fact, we give a manifestly gauge-invariant description of the Higgs mechanism
in the operator level, which does not rely on spontaneous symmetry breaking.
This enables us to discuss the confinement-Higgs complementarity from a new
perspective. The "Abelian" dominance in quark confinement of the Yang-Mills
theory is understood as a consequence of the gauge-invariant Higgs phenomenon
for the relevant Yang-Mills-Higgs model.
