Quark confinement and gauge invariant monopoles in SU(2) YM
  We give a short review of recently obtained results on a new lattice formulation of the non-linear change of variables which was once called the Cho--Faddeev--Niemi decomposition in SU(2) Yang-Mills theory.   Based on this formulation, we proposed a new gauge-invariant definition of the magnetic monopole current which guarantees the magnetic charge quantization. We also demonstrated the magnetic monopole dominance in the string tension in SU(2) Yang-Mills theory on a lattice. Our formulation enables one to reproduce in the gauge-invariant way remarkable results obtained so far only in the Maximally Abelian gauge. 
S. Kato, S.Ito, K.-I. Kondo, T. Murakami, A. Shibata and T. Shinohara