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In the rst part of this work, a perturbative analysis up to one-loop order is carried
out to determine the one-loop -function of noncommutative U(1) gauge theory with
matter elds in the adjoint representation. In the second part, the conformal anomaly
of the same theory is calculated using Fujikawa's path integral method. The value of
the one-loop -function calculated in both methods coincides. As it turns out, noncom-
mutative QED with matter elds in the adjoint representation is asymptotically free for
the number of
avor degrees of freedom Nf < 3.
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