Gauge-invariant gluon mass, infrared Abelian dominance, and stability of magnetic vacuum

We give an argument for deriving analytically the infrared Abelian dominance in a gauge-invariant way for the Wilson loop average in SU(2) Yang-Mills theory. In other words, we propose a possible mechanism for realizing the dynamical Abelian projection in the SU(2) gauge-invariant manner without breaking color symmetry. This supports validity of the dual superconductivity picture for quark confinement. We also discuss the stability of the vacuum with magnetic condensation as a by-product of this result.