Parametric representation of a translation-invariant renormalizable noncommutative model

Abstract

We construct here the parametric representation of a translation-invariant renormalizable scalar model on the noncommutative Moyal space of even dimension $D$. This representation of the Feynman amplitudes is based on some integral form of the noncommutative propagator. All types of graphs (planar and non-planar) are analyzed. The rôle played by noncommutativity is explicitly shown. This parametric representation established allows to calculate the power counting of the model. Furthermore, the space dimension $D$ is just a parameter in the formulas obtained. This paves the road for the dimensional regularization of this noncommutative model.

20 pages, 11 figures; the power counting dependence on the graph genus has been explicitly found; several misprints have been corrected; version accepted for publication to J. Phys. A: Math. Theor

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• Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term ${\sum }_s|p_s|+\mu$
• Energy momentum tensor for translation invariant renormalizable noncommutative field theory