Perturbative quantum gauge fields on the noncommutative torus

Using standard field theoretical techniques, we survey pure Yang-Mills theo ry on the noncommutative torus, including Feynman rules and BRS symmetry. A lthough in general free of any infrared singularity, the theory is ultravio let divergent. Because of an invariant regularization scheme, this theory t urns out to be renormalizable and the detailed computation of the one-loop counterterms is given, leading to an asymptotically free theory. Besides, i t turns out that nonplanar diagrams are overall convergent when theta is ir rational.