Nilpotent noncommutativity and renormalization

TL;DR

This paper investigates how bifermionic noncommutativity affects the renormalizability of noncommutative quantum field theories, introducing a new scalar model that remains renormalizable at all loop orders and analyzing NC QED's properties.

Contribution

It introduces a new 4D scalar model with bifermionic noncommutativity that is renormalizable at all orders and demonstrates improved renormalizability in NC QED.

Findings

New scalar model is renormalizable at all loop orders.

Bifermionic noncommutativity stabilizes infrared fixed points.

NC QED remains renormalizable at one-loop with bifermionic NC parameter.

Abstract

We analyze renormalizability properties of noncommutative (NC) theories with a bifermionic NC parameter. We introduce a new 4-dimensional scalar field model which is renormalizable at all orders of the loop expansion. We show that this model has an infrared stable fixed point (at the one-loop level). We check that the NC QED (which is one-loop renormalizable with usual NC parameter) remains renormalizable when the NC parameter is bifermionic, at least to the extent of one-loop diagrams with external photon legs. Our general conclusion is that bifermionic noncommutativity improves renormalizablility properties of NC theories.