Dimensional regularization and renormalization of non-commutative QFT

Using the recently introduced parametric representation of non-commutative quantum field theory, we implement here the dimensional regularization and renormalization of the vulcanized $\Phi^{\star 4}_4$ model on the Moyal space.Comment: 31 pages, 8 figure

Commutative limit of a renormalizable noncommutative model

Renormalizable $\phi^{\star 4}_4$ models on Moyal space have been obtained by modifying the commutative propagator. But these models have a divergent "naive" commutative limit. We explain here how to obtain a coherent such commutative limit for a recently proposed translation-invariant model. The mechanism relies on the analysis of the uv/ir mixing in general Feynman graphs.Comment: 11 pages, 3 figures, minor misprints being correcte

Translational-invariant noncommutative gauge theory

A generalized translational invariant noncommutative field theory is analyzed in detail, and a complete description of translational invariant noncommutative structures is worked out. The relevant gauge theory is described, and the planar and nonplanar axial anomalies are obtained.Comment: V1: 23 pages, 4 figures; V2: Section I. improved, References added. Version accepted for publication in PR

Non-trivial extension of the Poincar\'e algebra for antisymmetric gauge fields

We investigate a non-trivial extension of the $D-$dimensional Poincar\'e algebra. Matrix representations are obtained. The bosonic multiplets contain antisymmetric tensor fields. It turns out that this symmetry acts in a natural geometric way on these $p-$forms. Some field theoretical aspects of this symmetry are studied and invariant Lagrangians are explicitly given.Comment: LaTeX, 13 pages, contribution to the XI-th International Conference Symmetry Methods in Physics, Prague, June 21-24, 2004, presented by M. Rausch de Traubenber

Exorcizing the Landau Ghost in Non Commutative Quantum Field Theory

We show that the simplest non commutative renormalizable field theory, the $\phi^4$ model on four dimensional Moyal space with harmonic potential is asymptotically safe to all orders in perturbation theor