On the All Order Solutions of Seiberg-Witten Map for Noncommutative Gauge Theories

We review the recursive solutions of the Seiberg–Witten map to all orders in $\theta$ for gauge, matter and ghost fields. We also present the general structure of the homogeneous solutions of the defining equations. Moreover, we show that the contribution of the first order homogeneous solution to the second order can be written recursively similar to inhomogeneous solutions.