On the equivalence between noncommutative and ordinary gauge theories

Recently Seiberg and Witten have proposed that noncommutative gauge theorie s realized as effective theories on D-brane are equivalent to some ordinary gauge theories. This proposal has been proved, however, only for the Dirac -Born-Infeld action in the approximation of neglecting all derivative terms . In this paper we explicitly construct general forms of the 2n-derivative terms which satisfy this equivalence under their assumption in the approxim ation of neglecting (2n + 2)-derivative terms. We also prove that the D-bra ne action computed in the superstring theory is consistent with the equival ence neglecting the fourth and higher order derivative terms.