SPACETIME NONCOMMUTATIVITY WITH A BIFERMIONIC PARAMETER

Abstract

We consider a Moyal plane and propose to make the noncommutativity parameter Θμν bifermionic, i.e. composed of two fermionic (Grassmann odd) parameters. The Moyal product then contains a finite number of derivatives, which avoid the 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 problem with the canonical quantization and appears to be renormalizable.