Some remarks on Feynman rules for non-commutative gauge theories based on groups $G\ne U(N)$

Abstract

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 $G\subset U(N),G\ne U(M),M<N$ 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.

20 pages, LaTeX, 5 figures

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• Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups
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