Parametric representation of a translation-invariant renormalizable noncommutative model

Details Parametric representation of a translation-invariant renormalizable noncommutative model Parametric representation of a translation-invariant renormalizable noncommutative model

2008-07-17

arxiv.org/abs/0807.2779v2

J.Phys.A42:365208,2009

Physics

Mathematical Physics

20 pages, 11 figures; the power counting dependence on the graph genus has been explicitly found; several misprints have been

Scientific paper

10.1088/1751-8113/42/36/365208

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 r\^ole 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.

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