  In this article we expound a discovery of the quantum equivalence/duality of
U(N) noncommutative quantum field theories (NC QFT) related by the theta-exact
Seiberg-Witten (SW) maps and at all orders in the perturbation theory with
respect to the coupling constant. We show that this proof holds for Super
Yang-Mills (SYM) theories with N=0,1,2,4$ supersymmetry. In short,
Seiberg-Witten map does commute with the quantization of the U(N) NCQFT
independently, with or without supersymmetry.
