  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.
