Some remarks on Feynman rules for non-commutative gauge theories based   on groups $G\neq U(N)$
  We study for subgroups $G\subseteq U(N)$ partial summations of the $\theta$-expanded perturbation theory. On diagrammatic level a summation procedure is established, which in the U(N) case delivers the full star-product induced rules. Thereby we uncover a cancellation mechanism between certain diagrams, which is crucial in the U(N) case, but set out of work for $G\subset U(N)$. In addition, an explicit proof is given that for $G\subset U(N), G\neq U(M), M<N$ there is no partial summation of the $\theta $-expanded rules resulting in new Feynman rules using the U(N) star-product vertices and besides suitable modified propagators at most a $finite$ number of additional building blocks. Finally, we show that certain SO(N) Feynman rules conjectured in the literature cannot be derived from the enveloping algebra approach. 
Harald Dorn and Christoph Sieg (Humboldt University of Berlin)