The three-dimensional noncommutative Gross-Neveu model

TL;DR

This paper demonstrates that the noncommutative Gross-Neveu model becomes renormalizable and consistent when using a coherent basis representation, addressing previous issues with planar and nonplanar amplitude separation.

Contribution

It introduces a coherent basis approach to the noncommutative Gross-Neveu model, resolving its inconsistency and establishing conditions to control Lorentz symmetry breaking.

Findings

Model is renormalizable with coherent basis

Lorentz symmetry breaking is manageable with small noncommutativity

Provides insights on ordering prescriptions in noncommutative field theories

Abstract

This work is dedicated to the study of the noncommutative Gross-Neveu model. As it is known, in the canonical Weyl-Moyal approach the model is inconsistent, basically due to the separation of the amplitudes into planar and nonplanar parts. We prove that if instead a coherent basis representation is used, the model becomes renormalizable and free of the aforementioned difficulty. We also show that, although the coherent states procedure breaks Lorentz symmetry in odd dimensions, in the Gross-Neveu model this breaking can be kept under control by assuming the noncommutativity parameters to be small enough. We also make some remarks on some ordering prescriptions used in the literature.