The three-dimensional noncommutative Gross-Neveu model

Details The three-dimensional noncommutative Gross-Neveu model The three-dimensional noncommutative Gross-Neveu model

2006-05-23

arxiv.org/abs/hep-th/0605239v3

J.Phys.A40:3633-3642,2007

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/1751-8113/40/13/020

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.

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