The three-dimensional noncommutative Gross-Neveu model

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.

10 pages, IOP article style; v3: revised version, accepted for publication in J. Phys. A

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• Chern-Simons terms in Lifshitz like quantum electrodynamics
• Phase diagram of quark-antiquark and diquark condensates in the 3-dimensional Gross Neveu model with the 4-component spinor representation
• Black Holes Thermodynamics in a new kind of Noncommutative Geometry
• The Slavnov-Taylor Identities for the 2+1 Dimensional Noncommutative CP${}^{N-1}$ Model