Dimensional regularization and renormalization of non-commutative QFT

TL;DR

This paper applies dimensional regularization and renormalization techniques to a non-commutative quantum field theory model on Moyal space, utilizing a new parametric representation.

Contribution

It introduces a method to perform dimensional regularization and renormalization for non-commutative QFT using a novel parametric representation.

Findings

Successful regularization and renormalization of the vulcanized  model.

Extension of parametric representation to non-commutative QFT.

Enhanced understanding of non-commutative field theory renormalization.

Abstract

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.