Monopole dynamics of Yang-Mills theory without gauge-fixing

A new off-shell decomposition of SU(2) gauge field without any gauge fixing is proposed. This decomposition yields, for an appropriate gauge-fixing, a Skyrme-Faddeev-like Wilsonian action and confirms the presence of high-order derivatives of a color-unit-vector at the classical level. The 't Hooft's conjecture that ''monopole" dynamics of infrared Yang-Mills theory is projection independent is also independently demonstrated.