Gauge-independent derivation of "Abelian" dominance and magnetic monopole dominance in the string tension

Recently, we have developed a reformulation of the lattice Yang-Mills theory based on the change of variables a la Cho-Faddeev-Niemi combined with a non-Abelian Stokes theorem. In this talk, we give a new procedure (called reduction) for obtaining the color field which plays the central role in this reformulation. In the 4D SU(2) lattice Yang-Mills theory, we confirm the gauge-independent "abelian" dominance and gauge-independent magnetic-monopole dominance in the string tension extracted from the Wilson loop in the fundamental representation.