Lattice construction of Cho-Faddeev-Niemi decomposition and gauge   invariant monopole
  We present the first implementation of the Cho--Faddeev--Niemi decomposition of the SU(2) Yang-Mills field on a lattice. Our construction retains the color symmetry (global SU(2) gauge invariance) even after a new type of Maximally Abelian gauge, as explicitly demonstrated by numerical simulations. Moreover, we propose a gauge-invariant definition of the magnetic monopole current using this formulation and compare the new definition with the conventional one by DeGrand and Toussaint to exhibit its validity. 
S. Kato, K.-I. Kondo, T. Murakami, A. Shibata, T. Shinohara and S. Ito