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 . 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 is just a parameter in the formulas obtained. This paves the road for the dimensional regularization of this noncommutative model.
Cite
@article{arxiv.0807.2779,
title = {Parametric representation of a translation-invariant renormalizable noncommutative model},
author = {Adrian Tanasa},
journal= {arXiv preprint arXiv:0807.2779},
year = {2009}
}
Comments
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