  Motivated by Abelian dominance, we suppose that the field strength tensor in
the low energy limit of the SU(2) Yang-Mills theory is $ G_{\mu\nu}=G_{\mu\nu}
n $, where $ G_{\mu\nu} $ is a space-time tensor and $ n $ is a unit vector
field which selects the Abelian direction at each space-time point. Based on
this form of the field strength tensor, we propose a decomposition for the
Yang-Mills field with three degrees of freedom. It seems that by this kind of
decompostion, both monopoles and vortices appear at the same time. We have also
obtained the Dirac quantization condition with a rescaled electric charge.
