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

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