CP1-Fermion Correspondence in Three Dimensions

We show that in three dimensions the effective electromagnetic actions of the $C{P}^1$ model and of a charged fermion coincide in the vacuum and one-soliton sectors, to lowest order in inverse mass. This implies equivalence between the fermion and $C{P}^1$ current operators. In the vacuum sector, the first-order fermion-current-current self-interaction correction, required for equivalence at next-to-leading order, is also obtained. In the soliton phase, the two next to leading order terms appear with coefficients differing by simple numerical factors.