Scalar and gauge translation-invariant noncommutative models

Abstract

We make here a short overview of the recent developments regarding translation-invariant models on the noncommutative Moyal space. A scalar model was first proposed and proved renormalizable. Its one-loop renormalization group flow and parametric representation were calculated. Furthermore, a mechanism to take its commutative limit was recently given. Finally, a proposition for a renormalizable, translation-invariant gauge model was made.

6 pages, no figures

References in corpus (4)

• Vacuum configurations for renormalizable non-commutative scalar models
• On the vacuum states for noncommutative gauge theory
• 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
• Quantum Corrections for Translation-Invariant Renormalizable Non-Commutative Phi^4 Theory

Cited by in corpus (13)

• Combinatorial Dyson-Schwinger equations in noncommutative field theory
• Generalization of the Bollobás-Riordan polynomial for tensor graphs
• Noncommutative geometry, gauge theory and renormalization
• Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
• Curing the UV/IR mixing for field theories with translation-invariant $\star$ products
• On Non-Commutative U*(1) Gauge Models and Renormalizability
• Quantum Corrections for Translation-Invariant Renormalizable Non-Commutative Phi^4 Theory
• Some combinatorial aspects of quantum field theory
• One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative 1/p**2 U(1) Gauge Model
• Translation-Invariant Noncommutative Renormalization
• One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory
• Energy momentum tensor for translation invariant renormalizable noncommutative field theory
• star-Cohomology, Third Type Chern Character and Anomalies in General Translation-Invariant Noncommutative Yang-Mills