Space-time noncommutativity with a bifermionic parameter

TL;DR

This paper introduces a novel bifermionic noncommutativity parameter in a Moyal plane, leading to a finite-derivative Moyal product that simplifies analysis and results in a renormalizable, quantizable 2D noncommutative field theory with conserved energy-momentum.

Contribution

It proposes a bifermionic noncommutativity parameter to simplify the Moyal product and constructs a 2D noncommutative field theory demonstrating renormalizability and conserved quantities.

Findings

Finite-derivative Moyal product avoids standard difficulties.

Constructed 2D model has conserved energy-momentum tensor.

Model is compatible with canonical quantization and renormalization.

Abstract

We consider a Moyal plane and propose to make the noncommutativity parameter \Theta^{\mu\nu} bifermionic, i.e., composed of two fermionic (Grassmann odd) parameters. The Moyal product then contains a finite number of derivatives, which allows to avoid difficulties of the standard approach. As an example, we construct a two-dimensional noncommutative field theory model based on the Moyal product with a bifermionic parameter and show that it has a locally conserved energy-momentum tensor. The model has no problems with the canonical quantization and appears to be renormalizable.