  Recently Faddeev and Niemi proposed a low energy effective action for pure
SU(2) Yang Mills theory in 4 dimension to describe its long distance physics.
The effective action is O(3) $\sigma$ model with a mass parameter, a
dimensionless coupling constant e and a topological term. In this work,
choosing a new set of variables, we relate this $\sigma$ model to a U(1) gauge
theory with electric and magnetic charges of charge e and $4 \pi e^{-1}$
respectively. In the new formulation the connection of the mass parameter with
the monopole condensate is discussed. This theory after lattice regularisation
is the compact U(1) gauge theory coupled to electric charges.
