  We investigate the quantization of the theta-expanded noncommutative U(1)
Yang-Mills action, obtained via the Seiberg-Witten map. As expected we find
non-renormalizable terms. The one-loop propagator corrections are gauge
independent, and lead us to a unique extention of the noncommutative classical
action. We interpret our results as a requirement that also the trace in
noncommutative field theory should be deformed.
