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

References in corpus (14)

• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Noncommutative Induced Gauge Theory
• A translation-invariant renormalizable non-commutative scalar model
• Induced Gauge Theory on a Noncommutative Space
• Constructive ${\varphi }^4$ field theory without tears
• Vacuum configurations for renormalizable non-commutative scalar models
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• On the vacuum states for noncommutative gauge theory
• Translation-invariant models for non-commutative gauge fields
• Non-Commutative Complete Mellin Representation for Feynman Amplitudes
• Overview of the parametric representation of renormalizable non-commutative field theory
• Commutative limit of a renormalizable noncommutative model
• Parametric representation of "critical" noncommutative QFT models
• One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model