Annales Henri Poincaré

, Volume 8, Issue 3, pp 427–474

Renormalization of the Orientable Non-commutative Gross–Neveu Model

Open AccessArticle

DOI: 10.1007/s00023-006-0312-6

Cite this article as:
Vignes-Tourneret, F. Ann. Henri Poincaré (2007) 8: 427. doi:10.1007/s00023-006-0312-6


We prove that the non-commutative Gross–Neveu model on the two-dimensional Moyal plane is renormalizable to all orders. Despite a remaining UV/IR mixing, renormalizability can be achieved. However, in the massive case, this forces us to introduce an additional counterterm of the form \(\bar{\psi}\imath\gamma^{0}\gamma^{1}\psi\). The massless case is renormalizable without such an addition.

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© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique Bât. 210, CNRS UMR 8627Université Paris XIOrsay CedexFrance